Answer:
![-\frac{3p^8}{4q^3}](https://tex.z-dn.net/?f=-%5Cfrac%7B3p%5E8%7D%7B4q%5E3%7D)
Step-by-step explanation:
One is given the following expression,
![\frac{15p^-^4q^-^6}{-20p^-^1^2q^-^3}](https://tex.z-dn.net/?f=%5Cfrac%7B15p%5E-%5E4q%5E-%5E6%7D%7B-20p%5E-%5E1%5E2q%5E-%5E3%7D)
Since (15) and (-20) are both divisible by (5), one can divide both terms by (5) to simplify it.
![\frac{3p^-^4q^-^6}{-4p^-^1^2q^-^3}](https://tex.z-dn.net/?f=%5Cfrac%7B3p%5E-%5E4q%5E-%5E6%7D%7B-4p%5E-%5E1%5E2q%5E-%5E3%7D)
Now bring all of the terms with a negative exponent to the numerator. Multiply the exponents by (-1), then add them to the exponents of the like term in the numerator. Simplify the resulting exponents
![\frac{3p^-^4q^-^6}{-4p^-^1^2q^-^3}](https://tex.z-dn.net/?f=%5Cfrac%7B3p%5E-%5E4q%5E-%5E6%7D%7B-4p%5E-%5E1%5E2q%5E-%5E3%7D)
![\frac{3p^-^4^+^(^-^1^)^(^-^1^2^)q^-^6^+^(^-^1^)^(^-^3^)}{-4}](https://tex.z-dn.net/?f=%5Cfrac%7B3p%5E-%5E4%5E%2B%5E%28%5E-%5E1%5E%29%5E%28%5E-%5E1%5E2%5E%29q%5E-%5E6%5E%2B%5E%28%5E-%5E1%5E%29%5E%28%5E-%5E3%5E%29%7D%7B-4%7D)
![\frac{3p^-^4^+^1^2q^-^6^+^3}{-4}](https://tex.z-dn.net/?f=%5Cfrac%7B3p%5E-%5E4%5E%2B%5E1%5E2q%5E-%5E6%5E%2B%5E3%7D%7B-4%7D)
![\frac{3p^8q^-^3}{-4}](https://tex.z-dn.net/?f=%5Cfrac%7B3p%5E8q%5E-%5E3%7D%7B-4%7D)
Rewrite the fraction such that there are no negative exponents. Remember the rule, when bringing a number from the numerator to the denominator and back, multiply the exponent of the number by (-1). One can only switch numbers between the numerator and the denominator when all operations are multiplication or division.
![\frac{3p^8q^-^3}{-4}](https://tex.z-dn.net/?f=%5Cfrac%7B3p%5E8q%5E-%5E3%7D%7B-4%7D)
![-\frac{3p^8}{4q^3}](https://tex.z-dn.net/?f=-%5Cfrac%7B3p%5E8%7D%7B4q%5E3%7D)