Assuming that $x, y, z$ are positive real numbers, simplify each of the following:$ \left(\frac{x^{-4}}{y^{-10}}\right)^{5 / 4} $

Given:

\( \left(\frac{x^{-4}}{y^{-10}}\right)^{5 / 4} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

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

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$

Therefore,

$(\frac{x^{-4}}{y^{-10}})^{5 / 4}=x^{-4\times\frac{5}{4}} \times y^{10\times\frac{5}{4}}$

$=x^{-5} \times y^{\frac{25}{2}}$

$=\frac{y^{\frac{25}{2}}}{x^{5}}$

Hence, $(\frac{x^{-4}}{y^{-10}})^{5 / 4}=  \frac{y^{\frac{25}{2}}}{x^{5}}$.

Tutorialspoint

Updated on: 10-Oct-2022

27 Views

Kickstart Your Career

Get certified by completing the course

Get Started