Question

Express (13/21)2/5 as a radical

Answer 1

GIVEN :

The expression is $(\frac{13}{21})^{\frac{2}{5}}$

TO FIND :

The given expression in the radical form

SOLUTION :

Given expression is $(\frac{13}{21})^{\frac{2}{5}}$

To express the given expression as a radical:

$(\frac{13}{21})^{\frac{2}{5}}$

By using the formula in fractional exponent :

$(\frac{a}{b})^m=\frac{a^m}{b^m}$

$=\frac{(13)^{\frac{2}{5}}}{(21)^{\frac{2}{5}}}$

$=\frac{(13)^{2.(\frac{1}{5})}}{(21)^{2.(\frac{1}{5})}}$

By using the formula in fractional exponent :

$a^{mn}=(a^m)^n$

$=\frac{(13^2)^{\frac{1}{5}}}{(21^2)^{\frac{1}{5}}}$

$=\frac{(169)^{\frac{1}{5}}}{(441)^{\frac{1}{5}}}$

$=\frac{\sqrt[5]{169}}{\sqrt[5]{441}}$

By using the square root of division property:

For $b\neq 0$ $\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}$

$=\sqrt[5]{\frac{169}{441}}$

∴ $(\frac{13}{21})^{\frac{2}{5}}=\sqrt[5]{\frac{169}{441}}$

∴ the given expression $(\frac{13}{21})^{\frac{2}{5}}$ as a radical form is $\sqrt[5]{\frac{169}{441}}$

Answer 2

Answer :

5√169/144

explanation

done in square root method.