PRACTICE QUESTIONS ON RADICAL AND POWERS FOR SAT

(1)  9³ x 27² = 3ⁿ, n = ?            Solution

(2)  4^-a = 64, a = ?     Solution

(3)  x^-3 = 1/8, x = ?          Solution

(4)  5√8+7√32 = 

(a) 18√2  (b) 38√2  (c) 23√4  (d) 33√3  (e)  38√3

Solution

(5)  4√18 x 11√12 = 

(a) 12√6  (b) 34√6  (c) 264√6  (d) 264√3  (e)  264√2

Solution

(6)  y^-5 = 1024, y = ?              Solution

(7)  2^-n = 1/256, n = ?              Solution

(8)  √x = 4a²bc³, x = ?               Solution

(9)  8¹² = 2^x, x = ?                  Solution

(10)  c^2/5 = 4, c = ?          Solution

(11)  9^4x / 27^3x = ?

(a) 9^x  (b) 1/3^x  (c) 1/9x  (d) 3^x  (e)  1/4^x

Solution

(12)  Which of the following is equal to 5^8x?

I. (5^4x)⁴

II. (5^4x)²

III. (5^4x)(5^4x)

(a) I  (b) II    (c) III  (d)  I and II    (e)  II and III

Solution

(13)  n³ ≥ n² for which of the following?

I. n = 1

II. n = 0

III. n = −1

A. I   B. II   C. III   D. I and II   E. II and III

Solution

(14)  Simplify (a²b^-6c¹¹d^-4) / (a^-5b^-2c⁷d⁹)           Solution

(15)  27^4/x = 81, x = ?               Solution

(16)  3√x - 7 = 5, x = ?           Solution

(17)  9√x - 7√x - 36 = -16, x = ?

(a) 5   (b) 10   (c) 20   (d) 50  (e) 100

Solution

(18)  x = 2, y = x², (y²-x³)(x²/3y) = 

Solution

Problem 1 :

If x^c (3x)² / 9x³ = x⁶ and x ≠ 0, what is the value of c ?

Solution

Problem 2 :

x^5r/(x^{3r - 2s}) = x^t 

If r + s = 6 and x ≠ 0, what is the value of t in the equation shown ?

a)  6      b)  12    c)  18      d) 30

Solution

Problem 3 :

8 + [√(2x + 29) / 3] = 9

For what value of x is this equation true ?

a)  -10      b)  -2    c)  19      d) No solution

Solution

Problem 4 :

3x = x + 14

√(3z² - 11) + 2x = 22

If z > 0, what is the value of z ?

a)  1      b)  3    c)  5      d) 8

Solution

Problem 5 :

If n³ = -8, what is the value of (n²)³ / (1/n²)

Solution

Problem 6 :

Which of the following expression is equivalent to -x^1/4 ?

a)  -1/4x      b)  -1/x⁴        c) -∜x       d)  1/∜-x

Solution

Problem 7 :

√(3a + 16) - 3 = a - 1

In the equation above, if a ≥ 0, which of the following is possible value of a ?

a)  3      b)  2        c) 1      d)  0

Solution

Problem 8 :

√(4n² + 13) - y = 0

If n > 0 and y = 7 in the equation above, what is the value of n ?

a)  2     b)   3     c)  4      d)  5

Solution

Problem 9 :

If 5x - y = 7, what is the value of 32^x/2^y ?

a)  2⁷     b)   4⁷     c)  8³      d)  The answer cannot be determined

Solution

Problem 10 :

If √p + √16 = √81, what is the value of p ?

a)  2     b)   5     c)  9      d)  25

Solution