Question

What is `(4x^4y^-5z^4)/(6x^5yz^6)`?

Answer 1

`2/(3xy^6z^2)`

Explanation:

There are several ways to simplify indices, but they all involve applying the correct laws.

• Get rid of the negative index: `x^-m - 1/x^m`

`(4x^4color(blue)(y^-5)z^4)/(6x^5yz^6) = (4x^4z^4)/(6x^5ycolor(blue)(y^5)z^6)`

• Recall multiplying and dividing laws of indices:

`x^m xx x^n = x^(m+n) and x^m/x^n = x^(m-n)`

`(4x^4z^4)/(6x^5ycolor(blue)(y^5)z^6) = 2/(3xy^6z^2)`