Question

What is `(3xyz^2)/(6y^4)` by `(2y)/(xz^4)`?

Answer 1

`(3xyz^2)/(6y^4)*(2y)/(xz^4)=color(blue)(1/(y^2z^2)`

This answer came from multiplying the two expressions.

Explanation:

Simplify.

`(3xyz^2)/(6y^4)*(2y)/(xz^4)`

Combine both expressions.

`(3xyz^(2)2y)/(6y^4xz^4)`

Gather like terms.

`(3*2*x*y*y*z^(2))/(6*x*y^(4)z^(4))`

Cancel `6` and `x`.

`(color(red)cancel(color(black)(6))color(red)cancel(color(black)(x))y^(2)z^(2))/(color(red)cancel(color(black)(6))color(red)cancel(color(black)(x))y^(4)z^(4))`

`(y^(2)z^(2))/(y^(4)z^(4))`

Apply quotient exponent rule: `a^m/a^n=a^(m-n)`.

`(y^(2-4)z^(2-4))`

Simplify.

`y^(-2)z^(-2)`

Apply negative exponent rule: `a^(-m)=1/a^m`.

`1/(y^2z^2)`