Question

weeklyquiz - 9 5.1 - 5.3: proble
(1 point)
simplify the expression:
\\( \frac { - 2 a ^ { 9 } b ^ { - 4 } c ^ { - 3 } } { - 8 a ^ { - 1 } b ^ { 7 } c ^ { - 1 } } = \\)
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Explanation:

Step1: Simplify the coefficient

Simplify \(\frac{-2}{-8}\) to \(\frac{1}{4}\).

Step2: Use the rule \(x^m\div x^n=x^{m - n}\) for \(a\)

For \(a\) terms: \(a^{9}\div a^{-1}=a^{9-(-1)} = a^{10}\).

Step3: Use the rule \(x^m\div x^n=x^{m - n}\) for \(b\)

For \(b\) terms: \(b^{-4}\div b^{7}=b^{-4 - 7}=b^{-11}=\frac{1}{b^{11}}\).

Step4: Use the rule \(x^m\div x^n=x^{m - n}\) for \(c\)

For \(c\) terms: \(c^{-3}\div c^{-1}=c^{-3-(-1)}=c^{-2}=\frac{1}{c^{2}}\).

Answer:

\(\frac{a^{10}}{4b^{11}c^{2}}\)