Question

Simplify root 2 / 5 to the power 8 ÷ root 2 / 5 to the power 13

Answer 1

$\sqrt[]{ \frac{2}{5} }^{8} \div \sqrt[]{ \frac{2}{5} } ^{13}$

Answer 2

Concept

The definition of simplification is to simplify an expression, fraction, or difficulty.

In order to convert roots into powers, one must raise the radicand to the power of a fraction, where the radical's index will serve as the denominator and its exponent will be the fraction's exponent (typically 1).

Given

Given that $(\frac{\sqrt{2} }{5})^8$÷$({\frac{\sqrt{2} }{5} })^13$

Find

We need to simplify the equation

Solution

We need to simplify the equation $(\frac{\sqrt{2} }{5})^8$÷$({\frac{\sqrt{2} }{5} })^13$

= $(\frac{\sqrt{2} }{5})^8$×$({\frac{{5} }{\sqrt{2} } })^13$

= $(\frac{5}{\sqrt{2} })^5$

= $\frac{3125}{4\sqrt{2} }$

Hence the simplification is $\frac{3125}{4\sqrt{2} }$

#SPJ2