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

2 Answers
Jun 22, 2016

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

Explanation:

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

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

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

= 5^6

Jun 23, 2016

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