Question

Can you help me thank you

Answer 1

A.)
`(1)/(5^6)`

Explanation:

To simplify
`(5^2)^3`, use the exponent rule that states
`(a^m)^n=a^(mn)`

So,

`(5^2)^3=5^(2*3)=5^6`

Use the same exponent rule to begin simplifying
`(5^4)^(-3)`:

`(5^4)^(-3)=5^(4*(-3))=5^(-12)`

To further simplify
`5^(-12)`, use the exponent rule that states
`a^(-m)=(1)/(a^m)`

So,

`5^(-12)=(1)/(5^(12))`

Then multiply the two new expressions as indicated in the original problem:

`(5^6)((1)/(5^(12)))=(5^6)/(5^12)=(1)/(5^6)`

Alternatively, you could use the exponent rule that states
`a^m*a^n=a^(m+n)`

where

`a^m=5^6\\a^n=5^(-12)`

So,

`(5^6)(5^(-12))=5^(6+(-12))=5^(-6)=(1)/(5^6)`