EXPONENTS AND POWERS PRACTICE QUESTIONS FOR SAT

Problem 1 :

If 3^{x - 3} = 27, what is the value of x ?

(a)  0   (b)  3   (c)  6   (d)  9

Solution

Problem 2 :

If 27⁸¹ = 3^x, what is the value of x ?

(a)  27    (b)  84   (c)  100    (d) 243

Solution

Problem 3 :

If y > 0 and 

what is the value of b ?

(a) -3/2   (b)  -5/2   (c)  3/2    (d)  5/2

Solution

Problem 4 :

k² x^2a = x^{2a + 2}

In the equation above, k, x and a are positive integers greater than 1. What is the value of x - k ?

(a)  -1    (b)  0     (c)  1   (d) 2

Solution

Problem 5 :

x > 1, which of the following could be the value of a - b ?

(a)  3   (b)  4    (c)  5    (d)  6

Solution

Problem 6 :

If 

where n ≠ 0

Solution

Problem 7 :

The expression

where h > 0 and k > 0 is equivalent to which of the following ?

Solution

Problem 8 :

If c^-3d = 1/64 and c and d are positive integers, what is one possible value of d ?

Solution

Problem 9 :

Simplify the following :

Solution

Problem 10 :

If m = 1/√n, where m > 0 and n>0, what is n in terms of m ?

Solution

Problem 11 :

If c^-1/3 = x, where c > 0 and x > 0, then find the value of c in terms of x.

Solution

Problem 12 :

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

(a) -9    (b)  1/9   (c)  1/3   (d) 9

Solution

Problem 13 :

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

what is value of n ?

(a)  10   (b)  20   (c)  25   (d) 30

Solution

Problem 14 :

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

(a)  6   (b)  7   (c)  8    (d)  9

Solution

Problem 15 :

If 2^x/2^y = 2³, then x must equal 

(a) y + 3   (b)  y - 3    (c)  3 - y     (d)  3y

Solution

Problem 16 :

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

(a) -1   (b)  0    (c)  1     (d)  2

Solution

Problem 17 :

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

(a) -1   (b)  0    (c)  1     (d)  2

Solution

Problem 18 :

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

(a) 3   (b)  5    (c)  6     (d)  10

Solution