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

Mar 22, 2016

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
$\frac{3 {x}^{-} 4 {y}^{5}}{{2}^{-} 2 {x}^{-} 6 {y}^{14}}$

Now we can transpose the factors with negative exponents to the opposite side of the fraction bar to get:
$\frac{3 \left({2}^{2}\right) {x}^{6} {y}^{5}}{{x}^{4} {y}^{14}}$

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

$12 {x}^{2} {y}^{-} 9$

which is finally simplified to

$\frac{12 {x}^{2}}{{y}^{9}}$