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katie673

26.04.2023

Mathematics

$\frac{1}{125}$

Step-by-step explanation:

The given expression is

$(5^{-2}) (5^{-1})$

The expression is about two powers with the same base, so we can use the power property of multiplication, which states that we must proceed we writing only one base and sum exponents

$(5^{-2}) (5^{-1})=5^{-2-1}=5^{-3}$

Then, we use the negative exponent property

$5^{-3}=\frac{1}{5^{3} }$

Finally, we solve the power

$\frac{1}{5^{3} }=\frac{1}{125}$

Therefore, the given expression is equivalen to $\frac{1}{125}$ .

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