Which of the following represents fourth root of x cubed in exponential form? x to the three fourths power x to the four thirds power 4x3 3x4

Question

asked Dec 7, 2019 70.9k views

1 Answer

Dmreshet · Answer 1 · 2019-12-12T18:28:56+0000

Given: Fourth root of x cubed

To Find: The corresponding mathematical expression

Solution: The correct representation of the given statement is x to the three fourths power, i.e.
$x^{(3)/(4)}$

Step-by-step explanation:

The given statement is "fourth root of x cubed". We will take the statement step wise to construct the correct expression.

"Fourth root of x" corresponds to the expression
$\sqrt[4]{x}$ .

This may also be written as
$x^{(1)/(4)}$ .

Then, "fourth root of x cubed" means we have to cube the above ecpression, i.e., add the exponent 3.

So we will have
$(x^{(1)/(4)})^3$ .

Using the Rule of Exponents that for any integers a and b,
$(x^{(1)/(b)})^a= x^{(a)/(b)}$ , we can say

$(x^{(1)/(4)})^3=x^{(3)/(4)}$

So the correct representation of the given statement is x to the three fourths power.