How do you simplify #[ 3^2 / 3^ -1]^4#?

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Answer 1 · 2016-12-22T21:14:59

#3^12#

#[3^2/3^-1]^4#

first simplify the expression in brackets:

#[3^2/3^-1]#

#a^m/a^n = a^(m-n)#

using this law of indices:

#[3^2/3^-1] = 3^(2-(-1)) = 3^3#

this simplifies the whole expression to #(3^3)^4#

#(a^m)^n = a^(m*n)#

using this law of indices:

#(3^3)^4 = 3^(3*4) = 3^12#