Question

I Need Help Please ??!!

Answer 1

Step-by-step explanation:

The given statement is :

$\sqrt[4]{2} =2^{\dfrac{1}{4}}$

We need to select the correct simplification for this.

We know that, $\sqrt[a]{x} =x^{\dfrac{1}{a}}$

So,

$\sqrt[4]{2} =(2)^{\dfrac{1}{4}}$

Also, $(x^a)^b=x^{a\times b}$

So,

$(2^{\dfrac{1}{4}})^4=2^{\dfrac{1}{4}}\times 2^{\dfrac{1}{4}}\times 2^{\dfrac{1}{4}}\times 2^{\dfrac{1}{4}}\\\\=2^{\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}}\\\\=2^1\\\\=2$

So, these are the steps. Hence, the correct option is (B).