rewrite n sqrt x^m using a radical expression
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 \(\sqrt[n]{x^m}\) acn be rewrite as \((x)^{\times \frac{m}{n}}\)
Step-by-step explanation:
Given : \(\sqrt[n]{x^m}\)
We have to rewrite the given expression.
Consider the given expression \(\sqrt[n]{x^m}\)
Using property of exponent \(\sqrt[n]{x} =x^{\frac{1}{n}}\)
We have,
\(\sqrt[n]{x^m}=(x^m)^{\frac{1}{n}}\)
Again using property of exponents,\((x^a)^b=x^{ab}\)
We have ,
\((x^m)^{\frac{1}{n}}=(x)^{m\times \frac{1}{n}}\)
On simplifying, we get,
\((x)^{m\times \frac{1}{n}}=(x)^{\times \frac{m}{n}}\)
Thus, the given expression \(\sqrt[n]{x^m}\) acn be rewrite as \((x)^{\times \frac{m}{n}}\)