Respuesta :
The equivalent value of n * sqrt (x^m) can be written in exponent this would yield to n (x^m) ^ 1/ 2. This is raised to the power of one-half because its equivalence is a square root. A radical expression can be expressed thru radical and exponents.
Answer:
The given expression [tex]\sqrt[n]{x^m}[/tex] acn be rewrite as [tex](x)^{\times \frac{m}{n}}[/tex]
Step-by-step explanation:
Given : [tex]\sqrt[n]{x^m}[/tex]
We have to rewrite the given expression.
Consider the given expression [tex]\sqrt[n]{x^m}[/tex]
Using property of exponent [tex]\sqrt[n]{x} =x^{\frac{1}{n}}[/tex]
We have,
[tex]\sqrt[n]{x^m}=(x^m)^{\frac{1}{n}}[/tex]
Again using property of exponents,[tex](x^a)^b=x^{ab}[/tex]
We have ,
[tex](x^m)^{\frac{1}{n}}=(x)^{m\times \frac{1}{n}}[/tex]
On simplifying, we get,
[tex](x)^{m\times \frac{1}{n}}=(x)^{\times \frac{m}{n}}[/tex]
Thus, the given expression [tex]\sqrt[n]{x^m}[/tex] acn be rewrite as [tex](x)^{\times \frac{m}{n}}[/tex]
