How do you divide (-3x^2w)^3/(3x^4w^2)^4(−3x2w)3(3x4w2)4?

1 Answer
Stefan V.
Jul 25, 2015

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)(xn)m=xn⋅m

  • power of a product property

(x * y)^n = x^2 * y^n(x⋅y)n=x2⋅yn

  • quotient of powers property

(x^n)/(x^m) = x^(n-m)xnxm=xn−m, where x !=0x≠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(−3x2w)3=(−3)3⋅(x2)3⋅w3=−27⋅x6⋅w3

and

(3x^4w^2)^4 = 3^4 * (x^4)^4 * (w^2)^4 = 81 * x^(16) * w^8(3x4w2)4=34⋅(x4)4⋅(w2)4=81⋅x16⋅w8

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)))

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