How do i simplify (28x^3y^4z^-2)\(252xy^-2z^2)^3\2

Question

How do i simplify (28x^3y^4z^-2)\(252xy^-2z^2)^3\2

Answer 1

First the numbers....

252^(3/2) = ( 2*2*3*3*7)^(3/2) = [ 2 * 3 * sqrt(7) ] ^3 = 2^3 * 3^3 * sqrt(7)^3 = 8 * 27 * 7 * sqrt(3)=1512*sqrt(7)

Next the x:

x^3 / x^(3/2) = x^(3/2) since you subtract the exponents

Likewise, for the Y:

y^4 / y^(-2)^(3/2) = y^4 / y^(-3) = y^7

Finally the Z:

z^(-2) / (z^2^(3/2)) = z^(-2) / z^(3) = z^(-5)

The final answer is

1512*sqrt(7) * x^(3/2) * y^7 * z^(-5)

= 1512 * sqrt(7) * x^(3/2) * y^7 / z^5