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. [tex]x^{\frac{3}{4}}[/tex]
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 [tex]\sqrt[4]{x}[/tex].
This may also be written as [tex]x^{\frac{1}{4}}[/tex].
Then, "fourth root of x cubed" means we have to cube the above ecpression, i.e., add the exponent 3.
So we will have [tex](x^{\frac{1}{4}})^3[/tex].
Using the Rule of Exponents that for any integers a and b, [tex](x^{\frac{1}{b}})^a= x^{\frac{a}{b}}[/tex], we can say
[tex](x^{\frac{1}{4}})^3=x^{\frac{3}{4}}[/tex]
So the correct representation of the given statement is x to the three fourths power.
