Given expression in the simplest form of fraction is, [tex]\bold{\frac{5^{-1}}{-9^{0}} =\frac{1}{5}}[/tex]
"It is a number expressed as a quotient, in which a numerator is divided by a denominator."
"The fraction is in its simplest form, when the numerator and denominator of the fraction does not have any common factor."
For given example,
We have been given an expression [tex]\frac{5^{-1}}{-9^{0}}[/tex].
We need to evaluate [tex]\frac{5^{-1}}{-9^{0}}[/tex].
We know for any base if exponent is zero then its value is one.
So [tex]-9^0=1[/tex]
Also,[tex]5^{-1}=\frac{1}{5}[/tex]
So, given fraction becomes,
[tex]\frac{5^{-1}}{-9^{0}}[/tex]
= [tex]\frac{5^{-1}}{1}[/tex]
= [tex]5^{-1}[/tex]
= [tex]\frac{1}{5}[/tex]
Therefore, the fraction [tex]\frac{5^{-1}}{-9^{0}}[/tex] in simplest form is [tex]\bold{\frac{1}{5} }[/tex]
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