Question

Which expression is equivalent to -9x^-1y^-9/-15x^5y^-3? Assume x is not equal to 0,y is not equal to 0

a. 3/5x^5y^3
b. 3/5x^6v^6
c. 5/3x^5y^3
d. 5/3x^6y^6

Answer 1

I am going to assume that "v" is meant to be a "y"
the answer is b. (3)/(5x^6 y^6)

Answer 2

The correct option is b.

Explanation:

The given expression is

`(-9x^(-1)y^(-9))/(-15x^5y^(-3))`

It can be written as

`(-9)/(-15)* (x^(-1))/(x^5)* (y^(-9))/(y^(-3))`

Using the property of exponent we get

`(3)/(5)* x^(-1-5)* y^(-9+3)`
`[\because (x^m)/(x^n)=x^(m-n)]`

`(3)/(5)* x^(-6)* y^(-6)`

`(3)/(5)* (1)/(x^(6))* (1)/(y^(6))`
`[\because (1)/(x^n)=x^(-n)]`

`(3)/(5x^(6)y^(6))`

Therefore the correct option is b.