How do you use the laws of exponents to simplify the expression (-48x^4y^5z^2)/ (6x^2y^6z^4)−48x4y5z26x2y6z4?

1 Answer
Shura
May 17, 2015

The answer is : -(8x^2)/(yz^2)−8x2yz2

Let's separate your fraction :

(-48x^4y^5z^2)/(6x^2y^6z^4) = -48/6 * x^4/x^2 * y^5/y^6 * z^2/z^4−48x4y5z26x2y6z4=−486⋅x4x2⋅y5y6⋅z2z4.

Now, we will use the laws of exponents to simplify the last fractions :

-48/6 * x^4/x^2 * y^5/y^6 * z^2/z^4 = -8 * x^(4-2) * y^(5-6) * z^(2-4)−486⋅x4x2⋅y5y6⋅z2z4=−8⋅x4−2⋅y5−6⋅z2−4

= -8 * x^2 * y^(-1) * z^(-2) = -8*x^2*(1/y)*(1/z^2)=−8⋅x2⋅y−1⋅z−2=−8⋅x2⋅(1y)⋅(1z2)

=-(8x^2)/(yz^2)=−8x2yz2

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