Question

Which is equivalent to the cube root of 8^1/4x?

Answer 1

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Answer 2

Answer:

$2^{\frac{1}{4}x}$

Step-by-step explanation:

$\sqrt[3]{8^{\frac{1}{4}x}}$

The given radical expression can be written as exponential form

$\sqrt[n]{x} =x^{\frac{1}{n}}$

we write 8 in exponential form

$8=2*2*2= 2^3$

we apply the rule to convert it into exponential form

$\sqrt[3]{8^{\frac{1}{4}x}}=\sqrt[3]{2^{\frac{3}{4}x}}=2^{\frac{3}{4}x*\frac{1}{3}}=2^{\frac{1}{4}x}$