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.
Simplify $256^{3/4}$
$256^{3/4}$ = $\sqrt[4]{256^3}$ = $4^3$ = 64
Answer: $256^{3/4}$ = 64
Find $2^{1/4} \times 8^{1/4}$
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