Question

simplify.
\frac{a^{-7}b^{-4}c^{-6}}{a^{3}b^{2}c^{5}}
write your answer using only positive exponents.

Explanation:

Step1: Simplify \(a\) terms

For the variable \(a\), we use the rule \(\frac{a^m}{a^n}=a^{m - n}\). Here, \(m=-7\) and \(n = 3\), so \(a^{-7-3}=a^{-10}\). Using the rule \(a^{-n}=\frac{1}{a^n}\), this becomes \(\frac{1}{a^{10}}\).

Step2: Simplify \(b\) terms

For the variable \(b\), \(m = - 4\) and \(n=2\), so \(b^{-4 - 2}=b^{-6}=\frac{1}{b^{6}}\).

Step3: Simplify \(c\) terms

For the variable \(c\), \(m=-6\) and \(n = 5\), so \(c^{-6-5}=c^{-11}=\frac{1}{c^{11}}\).

Step4: Combine the terms

Multiply the simplified terms together: \(\frac{1}{a^{10}}\times\frac{1}{b^{6}}\times\frac{1}{c^{11}}=\frac{1}{a^{10}b^{6}c^{11}}\)

Answer:

\(\frac{1}{a^{10}b^{6}c^{11}}\)