Answer:
The simplified value of [tex]-25^{-\frac{1}{2}}[/tex] is [tex]-\frac{1}{5}[/tex].
Step-by-step explanation:
As the given expression is
[tex]-25^{-\frac{1}{2}}[/tex]
Lets simplify this expression step by step
As
[tex]-25^{-\frac{1}{2}}....[A][/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}[/tex]
[tex]25^{-\frac{1}{2}}=\frac{1}{25^{\frac{1}{2}}}[/tex]
So, lets plug [tex]25^{-\frac{1}{2}}=\frac{1}{25^{\frac{1}{2}}}[/tex] in equation [A] i.e. [tex]-25^{-\frac{1}{2}}....[A][/tex]
[tex]-25^{-\frac{1}{2}}....[A][/tex]
[tex]=-\frac{1}{25^{\frac{1}{2}}}[/tex] ∵ [tex]25^{-\frac{1}{2}}=\frac{1}{25^{\frac{1}{2}}}[/tex]
[tex]=-\frac{1}{5}[/tex] ∵ [tex]25^{\frac{1}{2}}=5[/tex]
Therefore, the simplified value of [tex]-25^{-\frac{1}{2}}[/tex] is [tex]-\frac{1}{5}[/tex].
Keywords: simplification, exponent rule
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