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Rational exponents are expressions with exponents that are rational numbers (as opposed to integers), where the numerator is a power and the denominator is a root.

Rules for rational exponents are similar to the rules of integer exponents.

Example 1:

Simplify $256^{3/4}$

Solution:

$256^{3/4}$ = $\sqrt[4]{256^3}$ = $4^3$ = 64

Answer: $256^{3/4}$ = 64

Example 2:

Find $2^{1/4} \times 8^{1/4}$

Solution:

Apply the Power of a Product rule:

$2^{1/4} \times 8^{1/4}$ = $(2 \times 8)^{1/4}$ = $16^{1/4}$

Now, we can rewrite $16^{1/4}$ as $\sqrt[4]{16}$

$\sqrt[4]{16}$ = 2

Answer: $2^{1/4} \times 8^{1/4}$ = 2