How do you simplify ((2x^3y^2) /( 3xy))^ -3?

2 Answers
Mar 25, 2016

27/(8x^3y^2)

Explanation:

The equation is raised to the negative third power, flip the fraction to turn it to a positive third power:

((2x^3y^2)/(3xy))^-3 = ((3xy)/(2x^3y^2))^3

Then raise the numerator and the denominator by the third power:

(3xy)^3/(2x^3y^2)^3

Distribute the third power exponent:

(3^3x^3y^3)/(2^3x^9y^6)

Factor an x^3y^3 from top and bottom:

((x^3y^3)(3^3))/((x^3y^3)(2^3x^3y^2))

Cancel out like terms from top and bottom:

(3^3)/(2^3x^3y^2)

Simplify: 27/(8x^3y^2)

Mar 26, 2016

27/(8x^6y^3)

Explanation:

For a moment let us disregard the power outside the brackets.

Example:" " 1/x^2 can be written as " "x^(-2)

So we have" " 2/3xxx^3y^2xxx^(-1)y^(-1)

This gives us:" "2/3xx x^(3-1)y^(2-1)

2/3xxx^2y = (2x^2y)/3

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Example: Suppose you have" " (1/x)^(-3) then this is" "(x/1)^3

Ok, so your question has: " "((2x^2y)/3)^(-3)

This gives us:" "(3/(2x^2y))^3

3^3= 27

2^3=8

(x^2)^3 =x^(2xx3) = x^6

(y)^3 = y^3

Putting it all together

27/(8x^6y^3)