Answer:
![-(3p^8)/(4q^3)](https://img.qammunity.org/2022/formulas/mathematics/high-school/cb0h9af0cxjfhde318ihzurauv86nsku24.png)
Explanation:
One is given the following expression,
![(15p^-^4q^-^6)/(-20p^-^1^2q^-^3)](https://img.qammunity.org/2022/formulas/mathematics/high-school/s9tt4tvgsvndk7250femrdahpjwzj1e9s5.png)
Since (15) and (-20) are both divisible by (5), one can divide both terms by (5) to simplify it.
![(3p^-^4q^-^6)/(-4p^-^1^2q^-^3)](https://img.qammunity.org/2022/formulas/mathematics/high-school/yqluy34l6svoo0s9pgyuvxbycymsqa0ehm.png)
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
![(3p^-^4q^-^6)/(-4p^-^1^2q^-^3)](https://img.qammunity.org/2022/formulas/mathematics/high-school/yqluy34l6svoo0s9pgyuvxbycymsqa0ehm.png)
![(3p^-^4^+^(^-^1^)^(^-^1^2^)q^-^6^+^(^-^1^)^(^-^3^))/(-4)](https://img.qammunity.org/2022/formulas/mathematics/high-school/f8o76sgifs85llp9jiy6b7s7ze6rnghiem.png)
![(3p^-^4^+^1^2q^-^6^+^3)/(-4)](https://img.qammunity.org/2022/formulas/mathematics/high-school/am71m5ioitxh4tni5blramrg8tp9dis15q.png)
![(3p^8q^-^3)/(-4)](https://img.qammunity.org/2022/formulas/mathematics/high-school/1hngz0csy66qhb2ox92lhe24xl875xk552.png)
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.
![(3p^8q^-^3)/(-4)](https://img.qammunity.org/2022/formulas/mathematics/high-school/1hngz0csy66qhb2ox92lhe24xl875xk552.png)
![-(3p^8)/(4q^3)](https://img.qammunity.org/2022/formulas/mathematics/high-school/cb0h9af0cxjfhde318ihzurauv86nsku24.png)