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, $(\frac{x^{-4}}{y^{-10}})^{5 / 4}= \frac{y^{\frac{25}{2}}}{x^{5}}$.
Related Articles
- Assuming that $x, y, z$ are positive real numbers, simplify each of the following:\( \sqrt[5]{243 x^{10} y^{5} z^{10}} \)
- Assuming that $x, y, z$ are positive real numbers, simplify each of the following:$\left(x^{-2 / 3} y^{-1 / 2}\right)^{2}$
- Assuming that $x, y, z$ are positive real numbers, simplify each of the following:$(\sqrt{x^{-3}})^{5}$
- Assuming that $x, y, z$ are positive real numbers, simplify each of the following:$\sqrt{x^{3} y^{-2}}$
- Assuming that $x, y, z$ are positive real numbers, simplify each of the following:\( \left(\frac{\sqrt{2}}{\sqrt{3}}\right)^{5}\left(\frac{6}{7}\right)^{2} \)
- Assuming that $x, y, z$ are positive real numbers, simplify each of the following:\( (\sqrt{x})^{-2 / 3} \sqrt{y^{4}} \p \sqrt{x y^{-1 / 2}} \)
- Assuming that $x,\ y,\ z$ are positive real numbers, simplify the following:$( x^{\frac{-2}{3}}y^{\frac{-1}{2}})^{2})$.
- Simplify each of the following expressions:\( (x+y+z)^{2}+\left(x+\frac{y}{2}+\frac{z}{3}\right)^{2}-\left(\frac{x}{2}+\frac{y}{3}+\frac{z}{4}\right)^{2} \)
- Find the following products:\( \frac{-4}{27} x y z\left[\frac{9}{2} x^{2} y z-\frac{3}{4} x y z^{2}\right] \)
- Factorize each of the following expressions:\( \left(\frac{x}{2}+y+\frac{z}{3}\right)^{3}+\left(\frac{x}{3}-\frac{2 y}{3}+z\right)^{3} +\left(-\frac{5 x}{6}-\frac{y}{3}-\frac{4 z}{3}\right)^{3} \)
- Find the following products:\( \left(\frac{x}{2}+2 y\right)\left(\frac{x^{2}}{4}-x y+4 y^{2}\right) \)
- Find the following products:\( 250.5 x y\left(x z+\frac{y}{10}\right) \)
- Find the following product.\( (-7 x y) \times\left(\frac{1}{4} x^{2} y z\right) \)
- Find the following products:\( \frac{-8}{27} x y z\left(\frac{3}{2} x y z^{2}-\frac{9}{4} x y^{2} z^{3}\right) \)
- \( \left(\frac{x}{2}+\frac{3 y}{4}\right)\left(\frac{x}{2}+\frac{3 y}{4}\right) \)
Kickstart Your Career
Get certified by completing the course
Get Started