Question

Rewrite the expression (5^-4)^2

Answer 1

`(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)`

Answer 2

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.