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Simplify the following expression. Write the answer without negative exponents and use only fractions if necessary (no decimals).

12^a−1b^10/−3a^−9b^−4

Oct 24, 2018

#1
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Simplify the following expression.
Write the answer without negative exponents and use only fractions if necessary (no decimals).

$$\begin{array}{|rcll|} \hline && \dfrac{12^{a-1}b^{10}}{-3a^{-9}b^{-4}} \\\\ &=& - \dfrac{12^{a-1}b^{10}}{3a^{-9}b^{-4}} \\\\ &=& - \dfrac{12^{a}12^{-1}b^{10}}{3a^{-9}b^{-4}} \\\\ &=& - \dfrac{12^{a}b^{10}}{3\cdot 12^1a^{-9}b^{-4}} \\\\ &=& - \dfrac{12^{a}b^{10}}{36a^{-9}b^{-4}} \\\\ &=& - \dfrac{12^{a}b^{10}a^{9}b^{4}}{36} \\\\ &=& - \dfrac{12^{a}a^{9}b^{10}b^{4}}{36} \\\\ &=& - \dfrac{12^{a}a^{9}b^{10+4}}{36} \\\\ &=& - \dfrac{12^{a}a^{9}b^{14}}{36} \\ \hline \end{array}$$

Oct 24, 2018