Question

simplify.
\frac{m^{-7}n^{-8}p^{-1}}{m^{6}n^{3}p^{5}}
write your answer using only positive exponents.

Explanation:

Step1: Apply exponent rule for division ($\frac{a^m}{a^n}=a^{m - n}$) to each variable.

For \( m \): \( m^{-7 - 6}=m^{-13} \)
For \( n \): \( n^{-8 - 3}=n^{-11} \)
For \( p \): \( p^{-1 - 5}=p^{-6} \)
So we have \( \frac{m^{-13}n^{-11}p^{-6}}{1} \) (since the coefficient is 1 in numerator and denominator for coefficients, we can ignore it for now).

Step2: Convert negative exponents to positive using \( a^{-n}=\frac{1}{a^n} \).

\( m^{-13}=\frac{1}{m^{13}} \), \( n^{-11}=\frac{1}{n^{11}} \), \( p^{-6}=\frac{1}{p^{6}} \)
Multiply these together: \( \frac{1}{m^{13}n^{11}p^{6}} \)

Answer:

\(\frac{1}{m^{13}n^{11}p^{6}}\)