Question

How do you simplify `(5^-2)^-3`?

Answer 1

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

Explanation:

As `(a^m)^n=a^(mxxn)`

`(5^(-2))^(-3)`

= `5^((-2)xx(-3))`

= `5^6`

Answer 2

`5^6`
With practice you could solve this in 1 to 2 lines. I have used a lot more than that to explain things.

Explanation:

`color(blue)("Step 1")" "`Dealing with just the brackets,

Consider just `5^(-2)`

This is stating that 5 is raised to the power of 2 but because we have negative 2 we have to invert it ( turn upside down ).

So write `5^(-2)" as "5^(-2)/1`

Note that writing as `5^(-2)/1` is not normally done but it is correct.

Inverting gives:

`1/5^(2) larr" Notice that the negative( minus) sign of -2 is now +2"`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 2")`

We now have: `(1/5^2)^(-3)`

Notice that both the numerator and denominator have this index applied.

Inverting

`(5^2/1)^3larr" The negative( minus) sign of -3 is now +3"`

`((5^2)^3)/(1)^3 = 5^(2xx3) = 5^6`