PRACTICE PROBLEMS ON RATIONAL EXPONENTS AND RADICALS

Simplify the following :

Problem 1 :

4^1/2

Solution

Problem 2 :

225^1/2

Solution

Problem 3 :

64^1/3

Solution

Problem 4 :

1000^1/3

Solution

Problem 5 :

81^1/4

Solution

Problem 6 :

32^1/5

Solution

Problem 7 :

8^-1/3

Solution

Problem 8 :

16^3/4

Solution

Problem 9 :

27^-2/3

Solution

Problem 10 :

(2  1/4)^-1/2

Solution

Problem 11 :

(3  3/8)^-2/3

Solution

Problem 12 :

Which expression is equivalent to

(x²y)(x⁴y^–3)

where x, y and z are positive numbers ?

A) x⁶y^–3     B) x⁶y^–2     C) x⁸y^–3    D) x⁸y^–2

Solution

Problem 13 :

Which expression is equivalent to

√(x/64) for all x > 0

A) x²/8     B) x²/32     C) √x/8    D) √x/32

Solution

Problem 14 :

Which expression is equivalent to

Which expression is equivalent to x^(5/6) / ∛x where x ≠ 0

A) x^1/2     B) x^5/2     C) x^2/3    D) x^5/3

Solution

Problem 15 :

If (5³)^4k = (5^1/3) ²⁴, what is the value of k ?

Solution

Problem 16 :

If a = 3√7/4 and 4a = √3b, what is the value of b ?

Solution

Problem 17 :

√(2c² - 4) + d = 1

If in the equation above, c > 0 and d = -1, what is the value of c ?

Solution

Problem 18 :

The expression is equivalent to a^2/9(a^2/3)^2/3, where a is positive?

Solution

Question 1 :

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

Solution

Question 2 :

If 9^x = 27⁸², what is the value of x?

Solution

Question 3 :

If y⁸ = m and y⁹ = 2/3, what is the value of y in terms of

Solution

Question 4 :

k²x^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?

Solution

Question 5 :

In the equation above, x > 1. Find the value of (a - b) such that (a - b) > 0.

Solution

Question 6 :

Which of the following is equal to ³√x² ⋅ √x³ ?

A) x     B) x^9/4    C) x^13/6    D) x³

Solution

Question 7 :

If 3√x³ = √72, what is the value of x?

Solution

Question 8 :

If 3x - y = 12, what is the value of 8^x ÷ 2^y?

Solution

Question 9 :

In the equation above, if x > 1 and a + b = 2, what is the value of (a - b)?

Solution

Question 10 :

In the expression above x > 1 and y > 1. Which of the following is equivalent to the above expression ?

Solution

Question 11 :

√(x - 2)² = √(3x + 34)

What is the smallest possible solution for x ?

Solution

Question 12 :

14x/7y = 2√(w + 19)

The given equation relates the distinct positive real numbers w, x, and y. Which equation correctly expresses w in terms of x and y ?

A)  w = √(x/y) - 19       B)  w = √(28x/14y) - 19

C)  w = (x/y)² - 19          D)  w = (28x/14y)² - 19

Solution

Problem 1 :

Find x so that

(-5)^x+1 ⋅ (-5)⁵  =  (-5)⁷

Solution

Problem 2 :

(5/3)^-2 ⋅ (5/3)^-14  =  (5/3)^8x

Solution

Problem 3 :

Find x so that

(-2)³ ⋅ (-2)^-6  =  (-2)^2x-1

Solution

Problem 4 :

Simplify

3⁰+3¹-3^-1

Solution

Problem 5 :

Simplify

(-125)^1/3

Solution

Problem 6 :

Simplify

(32)^2/5

Solution

Problem 7 :

Simplify

(64)^5/6

Solution

Problem 8 :

Simplify

(81)^-3/4

Solution

Problem 9 :

Simplify

3pq^-1

Solution

Problem 10 :

Simplify

(3^x ⋅ 9^x)/(27)^x+2 

Solution

Problem 11 :

Simplify

2^x ⋅ 8

Solution

Problem 12 :

Simplify

5ⁿ⁺²/5^n-2

Solution

Problem 13 :

Simplify

5^1+x/5^x-1

Solution

Problem 14 :

Simplify

8^x/16^y

Solution

Problem 15 :

Simplify

(5t^-2)^-1

Solution

Problem 16 :

Simplify

(xy)³/y^-2

Solution

Problem 17 :

Simplify

3^x-2  =  1/9

Solution

Problem 17 :

Simplify

3^x-2  =  1/9

Solution

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