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

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Answer 1 · 2016-06-22T08:36:32

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

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

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

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

= #5^6#

Answer 2 · 2016-06-23T09:53:50

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

#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#