Question

5.1 exponent prop
(1 point)
divide using the quotient rule of exponer
\\( \frac { 54 a ^ { 13 } b ^ { 16 } c ^ { 10 } } { 6 a ^ { 9 } b ^ { 12 } c ^ { 6 } } = \\)
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Explanation:

Step1: Divide the coefficients

According to the quotient rule for exponents \(\frac{a^m}{a^n}=a^{m - n}\) (\(a
eq0\), \(m,n\) are real numbers). For the coefficients, \(\frac{54}{6}=9\).

Step2: Apply the quotient rule for \(a\) - terms

For the \(a\) - terms, using \(\frac{a^{m}}{a^{n}}=a^{m - n}\), where \(m = 13\) and \(n=9\). So \(\frac{a^{13}}{a^{9}}=a^{13 - 9}=a^{4}\).

Step3: Apply the quotient rule for \(b\) - terms

For the \(b\) - terms, with \(m = 16\) and \(n = 12\). Then \(\frac{b^{16}}{b^{12}}=b^{16-12}=b^{4}\).

Step4: Apply the quotient rule for \(c\) - terms

For the \(c\) - terms, where \(m = 10\) and \(n = 6\). So \(\frac{c^{10}}{c^{6}}=c^{10 - 6}=c^{4}\).

Step5: Combine the results

Multiply the results from steps 1 - 4 together: \(9\times a^{4}\times b^{4}\times c^{4}=9a^{4}b^{4}c^{4}\).

Answer:

\(9a^{4}b^{4}c^{4}\)