Question

Rewrite the expression with rational exponents as a radical expression. 5 times x to the one fourth power

A. square root of the quantity 5 times x to the power of 4
B.fourth root of the quantity 5 times x
C. 5 times the square root of x to the power of 4
D.5 times the fourth root of x

Answer 1

Answer:

D

Step-by-step explanation:

We need to understand the rule shown below to solve this:

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

The expression to change is  $5*x^{\frac{1}{4}}$

The second part can be written as (using the rule):  $x^{\frac{1}{4}}=\sqrt[4]{x^1}=\sqrt[4]{x}$

And since 5 is a coefficient multiplied, we simply have :  $5*\sqrt[4]{x}$

Which is "5 times the fourth root of x", D is the correct answer.

Answer 2

Answer:

D.5 times the fourth root of x

Step-by-step explanation:

Given phrase,

5 times x to the one fourth power

$\implies 5\times (x)^\frac{1}{4}$

Since, a radical expression is defined as any expression containing a radical symbol i.e. '√'

Also,

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

Hence,

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

$\implies 5\times (x)^\frac{1}{4}=\sqrt[4]{x}$

= 5 times the fourth root of x

OPTION D is correct.