Question

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[tex]( \frac{3 {a}^{3} }{ {b}^{2} } ) \div ( \frac{27 {a}^{9} }{ {b}^{5} } )[/tex]
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Answer 1

Verified answer

[tex]\begin{align} \left( \frac{3 {a}^{3} }{ {b}^{2} } \right) \div \left( \frac{27 {a}^{9} }{ {b}^{5} } \right) &= \dfrac{3a^3}{b^2} \cdot \dfrac{b^5}{27a^9} \\ &= \dfrac{3a^3b^5}{27a^9b^2} \\ &= \dfrac{3}{27} a^{3-9}b^{5-2} \\ &= \dfrac{3}{3^3} a^{-6}b^3 \\ &= 3^{1-3}a^{-6}b^3 \\ &= 3^{-2}a^{-6}b^3 \\ &= \dfrac{b^3}{3^2a^6} \\ &= \dfrac{b^3}{9a^6} \end{align} [/tex]