Simplify (3x^7y^2)(2x^2y^7).

6x^9y^9

Simplify x^6 · x^3 (assume x ≠ 0).

x^9

Evaluate 2^5.

32

Multiply and simplify (7√3)(4√3).

84

Find the sum of the first 5 terms of a geometric sequence with a₁=-7 and r=4.

-2387

Rewrite x^(-6) using positive exponents (x ≠ 0).

1/x^6

A geometric sequence has a₄=-32 and common ratio 2. Find a₁.

-4

Find the sum of the first 15 terms of an arithmetic sequence with a₁=-2 and d=-5.

-555

Simplify (3x^5y^6)(2x^6y^5).

6x^11y^11

Simplify (3x^6y^5)(2x^5y^6).

6x^11y^11

Solve √(x + (7)) = 10. State the value of x and check that the radicand is nonnegative.

93

Multiply and simplify (4√5)(7√5).

140

Find the sum of the first 9 terms of a geometric sequence with a₁=4 and r=2.

2044

An arithmetic sequence has a_2=-12 and a_7=-17. Find its common difference.

-1

Solve √(x + (-6)) = 2. State the value of x and check that the radicand is nonnegative.

10

A geometric sequence has a₁=6 and common ratio r=4. Find a_6.

6144

Simplify (x^2)^5.

x^10

Evaluate 3^3.

27

Simplify (x^4)^3.

x^12

Evaluate 4^7.

16384

A geometric sequence has a₁=-3 and common ratio r=4. Find a_7.

-12288

An arithmetic sequence has a_5=-18 and a_10=-38. Find its common difference.

-4

Simplify √(117) completely.

3√13

Simplify 5√5 − 3√5.

2√5

Find the sum of the first 8 terms of a geometric sequence with a₁=4 and r=4.

87380

Simplify x^8/x^3 (assume x ≠ 0).

x^5

A geometric sequence has a₂=12 and a₃=24. Find the common ratio.

2

Solve √(x + (-6)) = 3. State the value of x and check that the radicand is nonnegative.

15

A geometric sequence has a₄=-16 and common ratio 2. Find a₁.

-2

Simplify 9√10 − 7√10.

2√10

Evaluate 6^2.

36

Simplify (3x^2y^5)(2x^5y^2).

6x^7y^7

Find the sum of the first 6 terms of a geometric sequence with a₁=4 and r=4.

5460

Solve √(x + (8)) = 8. State the value of x and check that the radicand is nonnegative.

56

Simplify (3x^5y^6)(2x^6y^5).

6x^11y^11

Simplify 9√5 − 6√5.

3√5

Solve √(x + (-7)) = 8. State the value of x and check that the radicand is nonnegative.

71

Simplify (x^7)^2.

x^14

An arithmetic sequence has a_8=-32 and a_11=-50. Find a₁.

10

Solve √(x + (-4)) = 6. State the value of x and check that the radicand is nonnegative.

40

Simplify x^3 · x^6 (assume x ≠ 0).

x^9

Find the sum of the first 9 terms of a geometric sequence with a₁=6 and r=2.

3066

Simplify √(500) completely.

10√5

A geometric sequence has a₄=-192 and common ratio 4. Find a₁.

-3

Simplify x^9/x^6 (assume x ≠ 0).

x^3

Solve √(x + (5)) = 11 over the real numbers.

116

Find the sum of the first 4 terms of a geometric sequence with a₁=-1 and r=2.

-15

Rewrite x^(-3) using positive exponents (x ≠ 0).

1/x^3

An arithmetic sequence has a₁=-11, d=8, and a_n=197. Which term number is n=27?

27

Simplify (3x^7y^4)(2x^4y^7).

6x^11y^11

An arithmetic sequence has a₁=13, d=-3, and a_n=-65. Which term number is n=27?

27

An arithmetic sequence has a_2=10 and a_9=38. Find its common difference.

4

An arithmetic sequence has a₁=-14, d=-1, and a_n=-40. Which term number is n=27?

27

Write an explicit formula for a geometric sequence with first term 2 and common ratio 3.

aₙ = 2(3)^(n−1)

Solve √(x + (5)) = 4. State the value of x and check that the radicand is nonnegative.

11

Find the sum of the first 24 terms of an arithmetic sequence with a₁=6 and d=5.

1524

An arithmetic sequence has a₁=-3, d=8, and a_n=157. Which term number is n=21?

21

Simplify x^9/x^4 (assume x ≠ 0).

x^5

Rewrite x^(-2) using positive exponents (x ≠ 0).

1/x^2

Simplify x^4 · x^2 (assume x ≠ 0).

x^6

Write an explicit formula for a geometric sequence with first term -3 and common ratio -3.

aₙ = -3(-3)^(n−1)

A geometric sequence has a₂=-9 and a₃=27. Find the common ratio.

-3

A geometric sequence has a₄=-448 and common ratio 4. Find a₁.

-7

A geometric sequence has a₄=54 and common ratio 3. Find a₁.

2

Solve √(x + (1)) = 7. State the value of x and check that the radicand is nonnegative.

48

Simplify √(18) completely.

3√2

A geometric sequence has a₄=189 and common ratio 3. Find a₁.

7

Find the sum of the first 27 terms of an arithmetic sequence with a₁=-12 and d=-3.

-1377

Simplify 8√2 − 5√2.

3√2

Simplify 4√10 − 2√10.

2√10

Simplify (3x^4y^5)(2x^5y^4).

6x^9y^9

An arithmetic sequence has a₁=-9 and common difference d=-6. Find a_16.

-99

A geometric sequence has a₁=1 and common ratio r=-3. Find a_5.

81

A geometric sequence has a₂=-3 and a₃=-9. Find the common ratio.

3

A geometric sequence has a₄=256 and common ratio 4. Find a₁.

4

Find the sum of the first 7 terms of a geometric sequence with a₁=2 and r=3.

2186

Find the sum of the first 17 terms of an arithmetic sequence with a₁=9 and d=2.

425

Simplify x^5 · x^6 (assume x ≠ 0).

x^11

An arithmetic sequence has a_7=-2 and a_10=1. Find a₁.

-8

Write an explicit formula for a geometric sequence with first term 1 and common ratio 4.

aₙ = 1(4)^(n−1)

Write an explicit formula for a geometric sequence with first term 7 and common ratio 3.

aₙ = 7(3)^(n−1)

A geometric sequence has a₁=-3 and common ratio r=-2. Find a_4.

24

Simplify √(40) completely.

2√10

A geometric sequence has a₂=-6 and a₃=12. Find the common ratio.

-2

An arithmetic sequence has a_6=8 and a_9=17. Find a₁.

-7

Simplify √(75) completely.

5√3

Find the sum of the first 6 terms of a geometric sequence with a₁=7 and r=-2.

-147

A geometric sequence has a₁=3 and common ratio r=2. Find a_5.

48

Multiply and simplify (3√3)(8√3).

72

A geometric sequence has a₂=16 and a₃=64. Find the common ratio.

4

Solve √(x + (19)) = 5 over the real numbers.

6

Simplify (x^2)^3.

x^6

An arithmetic sequence has a₁=15 and common difference d=6. Find a_18.

117

An arithmetic sequence has a₁=-15 and common difference d=1. Find a_19.

3

Simplify (x^5)^6.

x^30

Simplify x^9/x^3 (assume x ≠ 0).

x^6

An arithmetic sequence has a_6=4 and a_12=22. Find its common difference.

3

Write an explicit formula for a geometric sequence with first term -3 and common ratio 2.

aₙ = -3(2)^(n−1)

Simplify x^5 · x^2 (assume x ≠ 0).

x^7

Solve √(x + (16)) = 12 over the real numbers.

128

Simplify √(98) completely.

7√2

Simplify (x^2)^4.

x^8

Find the sum of the first 9 terms of a geometric sequence with a₁=5 and r=-2.

855

A geometric sequence has a₂=-8 and a₃=16. Find the common ratio.

-2

An arithmetic sequence has a_8=33 and a_11=48. Find a₁.

-2

A geometric sequence has a₁=3 and common ratio r=3. Find a_7.

2187

Simplify x^8/x^6 (assume x ≠ 0).

x^2

Find the sum of the first 9 terms of a geometric sequence with a₁=-6 and r=-2.

-1026

Simplify x^6/x^2 (assume x ≠ 0).

x^4

Rewrite x^(-5) using positive exponents (x ≠ 0).

1/x^5

An arithmetic sequence has a_7=26 and a_10=38. Find a₁.

2

An arithmetic sequence has a_7=22 and a_10=37. Find a₁.

-8

Simplify √(128) completely.

8√2

A geometric sequence has a₁=2 and common ratio r=4. Find a_6.

2048

Multiply and simplify (5√3)(6√3).

90

Multiply and simplify (2√5)(2√5).

20

Simplify (x^6)^3.

x^18

Simplify √(27) completely.

3√3

Evaluate 5^3.

125

Solve √(x + (13)) = 10 over the real numbers.

87

Solve √(x + (5)) = 8. State the value of x and check that the radicand is nonnegative.

59

An arithmetic sequence has a₁=-12 and common difference d=-5. Find a_28.

-147

Solve √(x + (9)) = 7 over the real numbers.

40

Simplify x^5 · x^2 (assume x ≠ 0).

x^7

Write an explicit formula for a geometric sequence with first term 3 and common ratio -2.

aₙ = 3(-2)^(n−1)

A geometric sequence has a₄=-24 and common ratio 2. Find a₁.

-3

An arithmetic sequence has a₁=3, d=-2, and a_n=-29. Which term number is n=17?

17

Simplify √(250) completely.

5√10

An arithmetic sequence has a_7=-20 and a_10=-26. Find a₁.

-8

An arithmetic sequence has a_2=-2 and a_6=-10. Find its common difference.

-2

Simplify 4√10 − 1√10.

3√10

Simplify (3x^5y^3)(2x^3y^5).

6x^8y^8

Simplify x^6/x^4 (assume x ≠ 0).

x^2

Rewrite x^(-2) using positive exponents (x ≠ 0).

1/x^2

Find the sum of the first 17 terms of an arithmetic sequence with a₁=3 and d=1.

187

An arithmetic sequence has a_8=11 and a_11=17. Find a₁.

-3

Multiply and simplify (8√5)(6√5).

240

Multiply and simplify (4√2)(5√2).

40

A geometric sequence has a₂=4 and a₃=16. Find the common ratio.

4

An arithmetic sequence has a_5=8 and a_8=20. Find a₁.

-8

Find the sum of the first 15 terms of an arithmetic sequence with a₁=10 and d=8.

990

Evaluate 3^7.

2187

Simplify x^4 · x^4 (assume x ≠ 0).

x^8

A geometric sequence has a₁=-4 and common ratio r=2. Find a_6.

-128

Simplify (x^5)^2.

x^10

A geometric sequence has a₂=-4 and a₃=-16. Find the common ratio.

4

Multiply and simplify (2√5)(4√5).

40

A geometric sequence has a₄=-189 and common ratio -3. Find a₁.

7

Multiply and simplify (3√7)(2√7).

42

An arithmetic sequence has a₁=10, d=-2, and a_n=-44. Which term number is n=28?

28

Solve √(x + (12)) = 5 over the real numbers.

13

An arithmetic sequence has a₁=7 and common difference d=-2. Find a_24.

-39

Solve √(x + (9)) = 3. State the value of x and check that the radicand is nonnegative.

0

A geometric sequence has a₄=-448 and common ratio 4. Find a₁.

-7

Simplify (3x^6y^3)(2x^3y^6).

6x^9y^9

Simplify √(1300) completely.

10√13

Simplify 5√10 − 4√10.

1√10

An arithmetic sequence has a₁=11, d=-5, and a_n=-34. Which term number is n=10?

10

A geometric sequence has a₂=4 and a₃=-8. Find the common ratio.

-2

A geometric sequence has a₂=-8 and a₃=16. Find the common ratio.

-2

An arithmetic sequence has a₁=2, d=7, and a_n=142. Which term number is n=21?

21

Simplify (3x^2y^4)(2x^4y^2).

6x^6y^6

Simplify x^7 · x^2 (assume x ≠ 0).

x^9

Write an explicit formula for a geometric sequence with first term 5 and common ratio -2.

aₙ = 5(-2)^(n−1)

An arithmetic sequence has a_4=7 and a_7=16. Find a₁.

-2

Simplify x^9/x^3 (assume x ≠ 0).

x^6

An arithmetic sequence has a₁=-10 and common difference d=-1. Find a_18.

-27

Simplify √(832) completely.

8√13

An arithmetic sequence has a₁=-2, d=6, and a_n=40. Which term number is n=8?

8

A geometric sequence has a₁=2 and common ratio r=2. Find a_7.

128

Simplify √(40) completely.

2√10

An arithmetic sequence has a₁=5 and common difference d=-4. Find a_9.

-27

Simplify 10√10 − 5√10.

5√10

Solve √(x + (1)) = 2. State the value of x and check that the radicand is nonnegative.

3

A geometric sequence has a₁=-6 and common ratio r=4. Find a_4.

-384

Simplify 5√10 − 2√10.

3√10

An arithmetic sequence has a_5=14 and a_8=32. Find its common difference.

6

Rewrite x^(-6) using positive exponents (x ≠ 0).

1/x^6

An arithmetic sequence has a₁=6 and common difference d=8. Find a_25.

198

Solve √(x + (0)) = 7 over the real numbers.

49

An arithmetic sequence has a₁=-1 and common difference d=5. Find a_14.

64

An arithmetic sequence has a₁=-4 and common difference d=8. Find a_27.

204

Simplify x^12/x^5 (assume x ≠ 0).

x^7

Solve √(x + (-10)) = 11 over the real numbers.

131

Find the sum of the first 24 terms of an arithmetic sequence with a₁=-3 and d=3.

756

Simplify √(1100) completely.

10√11

Simplify √(63) completely.

3√7

A geometric sequence has a₂=-6 and a₃=-18. Find the common ratio.

3

An arithmetic sequence has a_4=-31 and a_7=-52. Find its common difference.

-7

An arithmetic sequence has a_6=-25 and a_14=-81. Find its common difference.

-7

A geometric sequence has a₁=-7 and common ratio r=-3. Find a_9.

-45927

Find the sum of the first 15 terms of an arithmetic sequence with a₁=15 and d=3.

540

Simplify (3x^3y^5)(2x^5y^3).

6x^8y^8

An arithmetic sequence has a_5=5 and a_8=2. Find a₁.

9

Write an explicit formula for a geometric sequence with first term 1 and common ratio 4.

aₙ = 1(4)^(n−1)

A geometric sequence has a₂=9 and a₃=27. Find the common ratio.

3

A geometric sequence has a₂=-14 and a₃=-28. Find the common ratio.

2

An arithmetic sequence has a₁=-5, d=8, and a_n=139. Which term number is n=19?

19

Simplify (x^4)^5.

x^20

Write an explicit formula for a geometric sequence with first term 7 and common ratio 4.

aₙ = 7(4)^(n−1)

Simplify x^9/x^2 (assume x ≠ 0).

x^7

A geometric sequence has a₄=48 and common ratio -2. Find a₁.

-6

Simplify 5√2 − 4√2.

1√2

Evaluate 3^3.

27

Simplify 8√2 − 4√2.

4√2

An arithmetic sequence has a₁=0 and common difference d=-1. Find a_26.

-25

Simplify (x^3)^5.

x^15

Find the sum of the first 27 terms of an arithmetic sequence with a₁=15 and d=8.

3213

Multiply and simplify (7√3)(4√3).

84

Find the sum of the first 7 terms of a geometric sequence with a₁=-3 and r=3.

-3279

An arithmetic sequence has a_3=-1 and a_11=-25. Find its common difference.

-3

Rewrite x^(-4) using positive exponents (x ≠ 0).

1/x^4

Simplify (x^4)^5.

x^20

Solve √(x + (10)) = 9. State the value of x and check that the radicand is nonnegative.

71

Find the sum of the first 7 terms of a geometric sequence with a₁=-4 and r=-3.

-2188

A geometric sequence has a₂=18 and a₃=54. Find the common ratio.

3

Simplify (x^6)^4.

x^24

An arithmetic sequence has a_3=9 and a_12=45. Find its common difference.

4

Find the sum of the first 8 terms of an arithmetic sequence with a₁=16 and d=7.

324

An arithmetic sequence has a₁=10, d=4, and a_n=38. Which term number is n=8?

8

Simplify 10√7 − 4√7.

6√7

An arithmetic sequence has a₁=3 and common difference d=5. Find a_24.

118

Find the sum of the first 7 terms of a geometric sequence with a₁=-5 and r=3.

-5465

Evaluate 3^3.

27

Multiply and simplify (5√3)(3√3).

45

Rewrite x^(-6) using positive exponents (x ≠ 0).

1/x^6

Evaluate 4^6.

4096

Find the sum of the first 8 terms of a geometric sequence with a₁=1 and r=-2.

-85

An arithmetic sequence has a₁=13 and common difference d=-5. Find a_17.

-67

Solve √(x + (8)) = 4 over the real numbers.

8

An arithmetic sequence has a₁=-10 and common difference d=7. Find a_12.

67

Evaluate 5^4.

625

Find the sum of the first 12 terms of an arithmetic sequence with a₁=4 and d=3.

246

Simplify x^5 · x^6 (assume x ≠ 0).

x^11

An arithmetic sequence has a₁=-10 and common difference d=-5. Find a_22.

-115

Simplify (3x^3y^5)(2x^5y^3).

6x^8y^8

Solve √(x + (-5)) = 7 over the real numbers.

54

Find the sum of the first 6 terms of a geometric sequence with a₁=7 and r=-2.

-147

A geometric sequence has a₄=-128 and common ratio 4. Find a₁.

-2

Simplify x^4 · x^4 (assume x ≠ 0).

x^8

Simplify 3√2 − 1√2.

2√2

A geometric sequence has a₁=7 and common ratio r=2. Find a_5.

112

Multiply and simplify (6√5)(4√5).

120

Solve √(x + (7)) = 7 over the real numbers.

42

Find the sum of the first 9 terms of an arithmetic sequence with a₁=-12 and d=-8.

-396

A geometric sequence has a₁=-6 and common ratio r=-3. Find a_8.

13122

A geometric sequence has a₁=-1 and common ratio r=3. Find a_7.

-729

A geometric sequence has a₂=-12 and a₃=-24. Find the common ratio.

2

An arithmetic sequence has a_3=-7 and a_6=-10. Find its common difference.

-1

An arithmetic sequence has a₁=-4, d=8, and a_n=196. Which term number is n=26?

26

Simplify √(48) completely.

4√3

Solve √(x + (0)) = 10. State the value of x and check that the radicand is nonnegative.

100

Evaluate 2^3.

8

Rewrite x^(-5) using positive exponents (x ≠ 0).

1/x^5

Simplify x^2 · x^3 (assume x ≠ 0).

x^5

An arithmetic sequence has a_4=4 and a_7=19. Find a₁.

-11

Write an explicit formula for a geometric sequence with first term 6 and common ratio -3.

aₙ = 6(-3)^(n−1)

A geometric sequence has a₄=-40 and common ratio -2. Find a₁.

5

Write an explicit formula for a geometric sequence with first term -5 and common ratio 4.

aₙ = -5(4)^(n−1)

An arithmetic sequence has a_6=19 and a_9=31. Find a₁.

-1

Simplify x^8/x^2 (assume x ≠ 0).

x^6

Multiply and simplify (7√2)(5√2).

70

Multiply and simplify (8√7)(7√7).

392

An arithmetic sequence has a_6=-18 and a_10=-38. Find its common difference.

-5

Write an explicit formula for a geometric sequence with first term -1 and common ratio 2.

aₙ = -1(2)^(n−1)

Solve √(x + (-8)) = 2 over the real numbers.

12

An arithmetic sequence has a₁=6, d=-7, and a_n=-120. Which term number is n=19?

19

An arithmetic sequence has a_3=-11 and a_10=-39. Find its common difference.

-4

Write an explicit formula for a geometric sequence with first term -4 and common ratio 3.

aₙ = -4(3)^(n−1)

Simplify 6√5 − 3√5.

3√5

An arithmetic sequence has a₁=-13, d=7, and a_n=148. Which term number is n=24?

24

Rewrite x^(-4) using positive exponents (x ≠ 0).

1/x^4

Write an explicit formula for a geometric sequence with first term 3 and common ratio 4.

aₙ = 3(4)^(n−1)

Rewrite x^(-3) using positive exponents (x ≠ 0).

1/x^3

Solve √(x + (0)) = 10 over the real numbers.

100

Solve √(x + (11)) = 4 over the real numbers.

5

Rewrite x^(-5) using positive exponents (x ≠ 0).

1/x^5

Solve √(x + (-4)) = 5. State the value of x and check that the radicand is nonnegative.

29

Simplify 3√5 − 1√5.

2√5

Find the sum of the first 11 terms of an arithmetic sequence with a₁=-11 and d=1.

-66

An arithmetic sequence has a_5=17 and a_10=32. Find its common difference.

3

Simplify x^2 · x^4 (assume x ≠ 0).

x^6

A geometric sequence has a₁=6 and common ratio r=-3. Find a_8.

-13122

Find the sum of the first 8 terms of an arithmetic sequence with a₁=-8 and d=4.

48

An arithmetic sequence has a_3=-15 and a_6=-27. Find a₁.

-7

Solve √(x + (7)) = 10. State the value of x and check that the radicand is nonnegative.

93

Simplify x^3 · x^6 (assume x ≠ 0).

x^9

An arithmetic sequence has a_4=-1 and a_7=-13. Find a₁.

11

Evaluate 3^4.

81

Solve √(x + (7)) = 5 over the real numbers.

18

A geometric sequence has a₄=108 and common ratio 3. Find a₁.

4

Simplify (x^2)^6.

x^12

Multiply and simplify (6√7)(6√7).

252

A geometric sequence has a₄=-40 and common ratio -2. Find a₁.

5

Write an explicit formula for a geometric sequence with first term 5 and common ratio 3.

aₙ = 5(3)^(n−1)

Simplify x^7/x^2 (assume x ≠ 0).

x^5

Simplify x^11/x^4 (assume x ≠ 0).

x^7

An arithmetic sequence has a₁=-7, d=-1, and a_n=-24. Which term number is n=18?

18

An arithmetic sequence has a_5=18 and a_8=36. Find its common difference.

6

Find the sum of the first 13 terms of an arithmetic sequence with a₁=18 and d=-4.

-78