How do you multiply and simplify #(\frac { 2x y ^ { 2} \cdot - 2x ^ { 0} y ^ { 2} } { - 2x ^ { - 1} y ^ { 0} } ) ^ { 3}#?

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Answer 1 · 2018-06-26T03:35:32

The answer is #8x^6y^12#.

#((2xy^2*(-2x^0 y^2))/(-2x^-1 y^0))^3#

First, remember that anything raised to the 0th power is equal to #1#. So start by canceling out all the terms that are raised to #0#.

#((2xy^2 * (-2(1)y^2))/(-2x^-1(1)))^3#

#((2xy^2 * (-2y^2))/(-2x^-1))^3#

Multiply the numerator by adding the exponent of like terms. Don't forget the negative sign!

#((-4xy^4)/(-2x^-1))^3#

#((2xy^4)/(x^-1))^3#

Remember that anything raised to the #-1# is basically a reciprocal, so:

#x^-1 = 1/x#

Therefore:

#((2xy^4)/(1/x))^3 #

which is

#(2xy^4 * x)^3#

#(2x^2y^4)^3#

Distribute the exponent

#2^3 * x^(2 * 3) * y^ (4*3)#

#= 8x^6y^12#