Question

-25^-1/2 with explanation please

Answer 1

Answer:

The simplified value of $-25^{-\frac{1}{2}}$ is $-\frac{1}{5}$.

Step-by-step explanation:

As the given expression is

$-25^{-\frac{1}{2}}$

Lets simplify this expression step by step

As

$-25^{-\frac{1}{2}}....[A]$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

$25^{-\frac{1}{2}}=\frac{1}{25^{\frac{1}{2}}}$

So, lets plug $25^{-\frac{1}{2}}=\frac{1}{25^{\frac{1}{2}}}$ in equation [A] i.e.  $-25^{-\frac{1}{2}}....[A]$

$-25^{-\frac{1}{2}}....[A]$

$=-\frac{1}{25^{\frac{1}{2}}}$        ∵ $25^{-\frac{1}{2}}=\frac{1}{25^{\frac{1}{2}}}$

$=-\frac{1}{5}$           ∵ $25^{\frac{1}{2}}=5$

Therefore, the simplified value of $-25^{-\frac{1}{2}}$ is $-\frac{1}{5}$.

Keywords: simplification, exponent rule

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