Question

Which expression is equivalent to (256x16)1/4

Answer 1

Answer:

$4x^{4}$

Step-by-step explanation:

Given in the question an expression,

$(256x^{16})^\frac{1}{4}$

As we know that,

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

so

$\sqrt[4]{256x^{16} }$

it could also be written as

$\sqrt{\sqrt{256x^{16} } }$

First to solve inner square root

$\sqrt{256x^{16} } = 16x^{16/2}$

$\sqrt{16x^{8} }$

Second outer square root

$\sqrt{16x^{8}}=4x^{8/2}$=$4x^{4}$