How to Simplify Rational Exponents

Step-by-step solution

1. Read the denominator as a root.

   $$16^{3/4} = \left(16^{1/4}\right)^3$$

   Why: The fraction 3/4 means the fourth root, then the third power.

2. Take the fourth root first.

   $$16^{1/4} = 2$$

   Why: 2 times 2 times 2 times 2 is 16.

3. Raise the result to the third power.

   $$2^3 = 8$$

   Why: The numerator 3 is the power.

4. Write the answer.

   $$16^{3/4} = 8$$

   Why: The root and the power are both applied.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $8^{2/3}$

   Show answer

   $4$

2. 2

   $27^{1/3}$

   Show answer

   $3$

3. 3

   $25^{3/2}$

   Show answer

   $125$

4. 4

   $81^{1/2}$

   Show answer

   $9$

5. 5

   $32^{2/5}$

   Show answer

   $4$