How do you multiply 2x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}?

1 Answer
Aug 22, 2017

See below.

Explanation:

Let's deal with the value inside the parenthesis first.

2x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}

Remember that x^-a=1/x^a

( 9x ^ { 3} y ) ^ { - 3}=9^-3x^-9y^-3=1/(729x^9y^3)

Combining,

2x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}=2x ^ { 2} y ^ { 5} *1/(729x^9y^3)

x^a/x^b=x^(a-b)

So,

2x ^ { 2} y ^ { 5} *1/(729x^9y^3)=\frac(2y^2)(729x^7)

Since 2 and 9 have no common multiples, this is our solution.