Question

How do you simplify `\frac { 7x ^ { 4} y ^ { 2} } { 8z } \cdot \frac { 12z ^ { 3} } { 21x ^ { 2} y ^ { 3} }`?

Answer 1

`( x^2  z^2) / (2 y)`

Explanation:

This is just one long multiplication divided by another.

For your own convenience, write these as one long numerator over one long denominator.

If you stack the like variables, it will be easy to cancel them to reduce this fraction to lowest terms.

`(7x^4y^2)/(8z)⋅(12z^3)/(21x^2y^3)`

1) Re-write the given expression as one long numerator over one long denominator, stacking like factors

`(color(white)(...)7 * 12 * x^4 * y^2 * z^3)/(21 * 8* x^2 * y^3 * z )`

2) Cancel

`(color(white)(.....)cancel(7) color(white)(.)* color(white)(.)cancel(12)(3) * color(white)(. )cancel(x^4)^2 color(white)(.) * cancel(y^2) * color(white)(.)cancel(z^3)^2)/( color(white)()cancel(21)(3) * color(white)(.)cancel(8)(2) color(white)(.) * color(white)(.)cancel(x^2) *   color(white)(.)y^1     * cancel(z) )`

Cancel again

`(cancel(3) * x^2 * z^2) / (cancel(3) * 2 * y)`

Answer:

`( x^2  z^2) / (2  y)`