Question

How do you simplify `(3x^-4y^5)/(2x^3y^-7)^-2` using only positive exponents?

Answer 1

order of operations requires that we deal with the exponent in the denominator first using the power to power rule.
this means that our expression now becomes
`(3x^-4 y^5)/(2^-2x^-6y^14)`

Now we can transpose the factors with negative exponents to the opposite side of the fraction bar to get:
`(3(2^2) x^6 y^5)/(x^4y^14)`

which now makes everything simple by using the subtraction rule for exponents when we divide with the same base.

`12x^2y^-9`

which is finally simplified to

`(12 x^2)/(y^9)`