How do you simplify #(\frac { 2a ^ { - 1} b ^ { 5} } { 3b ^ { - 5} a ^ { - 6} } ) ^ { - 3}#?

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Answer 1 · 2017-06-25T01:46:29

#27/8a^-15b^-30=27/(8a^15b^30)#

Let's first evaluate what's inside the bracket, then apply the exponent:

We'll first be using the rule #x^a/x^b=x^(a-b)#

#((2a^-1b^5)/(3b^-5a^-6))^-3#

#(2/3a^(-1-(-6))b^(5-(-5)))^-3#

#(2/3a^5b^10)^-3#

And now we use the rule #(x^a)^b=x^(ab)#

#(2/3)^-3a^(5xx-3)b^(10xx-3)#

#(2^-3/3^-3)a^-15b^-30#

#(1/8)/(1/27)a^-15b^-30#

#27/8a^-15b^-45=27/(8a^15b^30)#