How do you simplify #(\frac { 7x ^ { 5} } { y ^ { 2} } ) ^ { - 3}#?

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Answer 1 · 2018-01-25T06:36:44

The answer is #y^6/(343x^15)#

First, distribute overall exponent to the numerator and the denominator for the big fraction:

#((7x^5)/y^2)^-3=>((7x^5)^-3)/(y^2)^-3#

Then, distribute each of those new exponents onto their bases:

#((7x^5)^-3)/(y^2)^-3=> (7^-3*(x^5)^-3)/y^-6=>(7^-3*x^-15)/y^-6#

Next, if there are any negative exponents on the bottom, bring them to the top and make the positive, and vice versa:

#(7^-3*x^-15)/y^-6=>y^6/(7^3*x^15)#

7 cubed simply equals 343, so your final answer is

#y^6/(343*x^15)#