How do you simplify #(\frac { w ^ { 4} } { 3} ) ^ { - 3}#?

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Answer 1 · 2018-04-21T17:55:59

#(w^4/3)^-3=27/w^12#

In order to simplify #(w^4/3)^-3#

Begin by distributing the exponent outside the parenthesis to both the numerator and the denominator

#((w^((4)(-3)))/3^-3#

This gives us #(w^-12/3^-3)#

In order to eliminate the negative exponents invert numerator and the denominator

#3^3/w^12#

Now simplify the exponent value in the numerator #3^3 = 27#

#27/w^12#

Answer 2 · 2018-04-21T18:30:26

#=27/w^12#

By applying the laws of indices:

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

#(w^4/3)^-3 = (3/w^4)^3#

Now raising each factor in the bracket to the power of #3# gives:

#3^3/w^(4xx3)#

#=27/w^12#