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Rewrite the expression (5^-4)^2

User Ricecakes
by
7.9k points

2 Answers

5 votes

Answer:


(1)/(390625)

Explanation:

(5^-4)^2

Multiply the exponents in (5^-4)^2


5^(8)

Rewrite the expression using the negative exponent rule
b^(-n) =
(1)/(b^(n) )


(1)/(5^(8) )

Raise 5 to the power of 8.


(1)/(390625)

User Jo Paul
by
8.2k points
4 votes

The answer is:


\sf{(1)/(5^8)}

Work/explanation:

Remember that if we raise a power to a power, we multiply the powers.

This can be shown with the law
\sf{(x^m)^n}=x^(m+n)}

Simplify


\sf{(5^(-4))^2=5^(-4\cdot2)=5^(-8)

Now, let's shift our attention to the next exponent law:


\sf{x^(-m)=(1)/(x^m)}

Similarly,


\sf{5^(-8)=(1)/(5^8)}

Hence, that's the answer.

User Sbaechler
by
8.5k points

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