SAT Math Problems on Exponents and Radicals

Problem 1 :

Let n = 1² + 1⁴ + 1⁶ + 1⁸ + .......... + 1⁵⁰.

What is the value of n?

A)  10

B)  20

C)  25

D)  30

Problem 2 :

If x² = y³, for what value of z does x^3z = y⁹?

A)  -1

B)  0

C)  1

D)  2

Problem 3 :

If 2^{x + 3} - 2^x = k(2^x), what is the value of k?

A)  3

B)  5

C)  7

D)  8

Problem 4 :

If √(x√x) = x^a, then what is the value of a?

A)  1/2

B)  3/4

C)  1

D)  4/3

Problem 5 :

If x^ac ⋅ x^ac = x³⁰, x > 1 and a + b = 5, what is the value of c?

A)  3

B)  5

C)  6

D)  10

Problem 6 :

If n³ = x and n⁴ = 20x, where n > 0, what is the value of x?

Problem 7 :

If x⁸y⁷ = 333 and x⁷y⁶ = 3, what is the value of xy?

Problem 8 :

2√(x + 2) = 3√2

If x > 0 in the equation above, what is the value of x?

A)  2.5

B)  3

C)  3.5

D)  4

Problem 9 :

If 2a - b = 4, what is the value of 4^a/2^b?

Problem 10 :

If √x + √y = 4√y, where x > 0 and y > 0, what is x in terms of y?

A)  16y

B)  9y

C)  6y

D)  4y

Answers (1 - 10)

Problem 11 :

If a^-1/2 = 3, what is the value of a?

A)  -9

B)  ⅑

C)  ⅓

D)  9

Solution :

Problem 12 :

Which expression is equivalent to 2^-2k ⋅ 3^k?

A)  (3√2)^k

B)  (1/36)^k

C)  (3/4)^k

D)  (9/4)^k

Solution :

Problem 13 :

If 4^{2n + 3} = 8^{n + 5}, what is the value of n? 

A)  10

B)  20

C)  25

D)  30

Solution :

Problem 14 :

If 3^x = 10, what is the value of 3^{x - 3}?

A)  ¹⁰⁄₃

B)  ¹⁰⁄₉

C)  ¹⁰⁄₂₇

D)  ²⁷⁄₁₀

Solution :

Problem 15 :

If x²y³ = 10 and x³y² = 8, what is the value of x⁵y⁵?

A)  18

B)  20

C)  40

D)  80

Solution :

Problem 16 :

If a and b are positive integers, which of the following is greatest?

A)  (-2a)^b

B)  (-2a)^2b

C)  (2a)^b

D)  2a^2b

Solution :

Problem 17 :

If x¹⁰ = 5 and x⁹/y = 5555, find the value of 1/xy.

A)  5

B)  1111

C)  2525

D)  5555

Solution :

Problem 18 :

A)  2¹²

B)  4⁴

C)  8²

D) The value can not be determined from the information given

Solution :

Problem 19 :

Solution :

Problem 20 :

If (300)(400) = 12 ⋅ 10ⁿ, what is the value of n?

Solution :

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