Question

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

• A. True
• B. False
• C. Do not say
• D. None of these

Answer 1

The correct option is A True

Let ${\sqrt[m]{mx}}^n=p$

$⟹x^n=p^m$

$x={\sqrt[n]{np}}^m$

Now substitute $x$ in $x^{\frac{n}{m}}$

so

$x^{\frac{n}{m}}=({\sqrt[n]{np}}^m{)}^{\frac{n}{m}}$ $(a^m{)}^n=a^{mn}$

$=p^{\frac{n}{m}\ast \frac{m}{n}}$

$=p$

$\therefore {\sqrt[m]{mx}}^n=p=x^{\frac{n}{m}}$

hence, it is TRUE