Question

What is `(20x^4y^2z^3)/(4x^2y^2z)`?

Answer 1

When dividing exponents, you really subtract the degree of the exponent. This is because you can expand out the expression and cancel the x, y, and z's out. (Try for yourself if you'd like).

So, the x's cancel out to leave `x^2` in the numerator
All of the y's cancel out
and the z cancels out leaving `z^2` in the numerator

And we know how to divide numbers, so `20/4 = 5`

And we put all these pieces together

Our answer is `5x^2z^2`

Answer 2

`=color(brown)(5x^2z^2`

Explanation:

`color(blue)((20x^4y^2z^3)/(4x^2y^2z)`

Try to cancel everything:

`rarr=color(green)((cancel(20)x^4y^2z^3)/(cancel(4)x^2y^2z)`

`rarr=color(green)((5cancel(x^4)y^2z^3)/(cancel(x^2)y^2z)`

`rarr=color(green)((5x^2cancel(y^2)z^3)/(cancel(y^2)z)`

`rarr=color(green)((5x^2cancel(z^3))/(cancelz)`

`rArr=color(brown)(5x^2z^2`