Question

Simplify the expression:
The picture is down below

Answer 1

`(4x^(21))/(y^(11))`

Explanation:

You are going to need to know two properties of exponents.

`x^a * x^b = x^(a+b)\\(x^a)/(x^b)=x^(a-b)`

Also know that a*b = b*a, so youc an change the order of multiplication.

Since everything is being multiplied in the numerator, and there is only multiplication, it's actually super easy to start. Just multiply everything.

`8x^9y^8(-2)x^5y^(-9) = -16x^(14)y^(-1)`

so now you have
`(-16x^14y^(-1))/(-4x^(-7)y^6)`

Again, since the numerator and denominator only have multiplication you can divide part by part. so the number divides the number, the x term divides the term and the y term divides the y term

-16/-4 = 4

x^14 / x^-7 = x^21

y^-1 / y^6 = y^-7

So all together that makes
`4x^(21)y^(-7)`

The final step in simplifying is making all negative powers into fractions. Sometimes non whole numbers can be made into roots. Definitely make negative powers fractions though

`(4x^(21))/(y^(-7))`