Question

How do you divide `(-3x^2w)^3/(3x^4w^2)^4`?

Answer 1

You use three properties of exponents to rewrite the numerator and denominator, and cancel out common terms.

Explanation:

Three properties of exponents will come in handy for this problem

• power of a power property

`(x^n)^m = x^(n * m)`

• power of a product property

`(x * y)^n = x^2 * y^n`

• quotient of powers property

`(x^n)/(x^m) = x^(n-m)`, where `x !=0`

Using these three properties will allow you to rewrite the numerator and denominator as

`(-3x^2w)^3 = (-3)^3 * (x^2)^3 * w^3 = -27 * x^6 * w^3`

and

`(3x^4w^2)^4 = 3^4 * (x^4)^4 * (w^2)^4 = 81 * x^(16) * w^8`

The expression will now become

`( -cancel(27) * x^6 * w^3)/(cancel(27) * 3 * x^(16) * w^8) = -(x^6 * w^3)/(3 * x^(16) * w^8)`

Finally, the expression becomes

`-(x^6 * w^3)/(3 * x^(16) * w^8) = color(green)(-1/(3 * x^(10) * w^(5)))`