How do you multiply #a^(-4)*(a^4b^3)^3#?

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Answer 1 · 2015-04-06T22:52:38

#a^-4(a^12b^9)#

Since #a^-4 = 1/a^4#
#(a^12b^9)/a^4#

When you divide exponents with the same base, you can subtract them:
#a^8b^9#

Answer 2 · 2015-04-06T23:37:05

The result is #a^8b^9#.

#a^(-4)*(a^4b^3)^3#

Take care of the parentheses first.
#(a^4b^3)^3#

Multiply the exponent outside the parentheses by each of the exponents inside the parentheses.

#(a^(4xx3)b^(3xx3)) = (a^12b^9)#

Now multiply the bases a and b and add the exponents on like bases.

#a^(-4)*(a^12b^9)# =

#a^(-4+12)(b^9)# =

#a^8b^9#

Another way to multiply these terms is to use the inverse of #a^(-4)#.

#a^(-4)=(1)/(a^4)#

#(a^12b^9)/(a^(4))#

Subtract the exponent on base a in the denominator from the exponent on base a in the numerator.

#a^(12-4)b^9# = #a^8b^9#