Question

Simplify the following
4√(256)^-2

Answer 1

Answer:

(256^-2)^1/4

= (1/256)2/4

= (1/256)^1/2

= [(1/16)^2]^1/2

= (1/16)

Answer 2

The expression is $(\sqrt[4]{256})^{-2}=\frac{1}{16}$

Step-by-step explanation:

Given : Expression $(\sqrt[4]{256})^{-2}$

To find : Simplify the expression ?

Solution :

We know that, $\sqrt[n]{x}=x^{\frac{1}{n}}$

Applying in the expression,

$(\sqrt[4]{256})^{-2}=(256)^{-\frac{2}{4}}$

$(\sqrt[4]{256})^{-2}=(256)^{-\frac{1}{2}}$

$(\sqrt[4]{256})^{-2}=(16^2)^{-\frac{1}{2}}$

$(\sqrt[4]{256})^{-2}=(16)^{-1}$

$(\sqrt[4]{256})^{-2}=\frac{1}{16}$

Therefore, the expression is $(\sqrt[4]{256})^{-2}=\frac{1}{16}$

#Learn more

Simplify (256)^-(4^-3/2)

https://brainly.in/question/1206129