Answer
$=\frac{−27b^{15}}{a^{18}}$
Work Step by Step
$$(\frac{−15a^{4}b^{2}}{5a^{10}b^{-3}})^{3}$$
Recall the power rule: $(a^{m})^{n}=a^{mn}$
Thus,
$=(\frac{−15a^{4}b^{2}}{5a^{10}b^{-3}})^{3}$
$=(\frac{−3a^{4}b^{2}}{a^{10}b^{-3}})^{3}$
$=\frac{−3^{3}a^{4\cdot 3}b^{2\cdot 3}}{a^{10\cdot 3}b^{-3\cdot 3}}$
$=\frac{−3^{3}a^{12}b^{6}}{a^{30}b^{-9}}$
$=\frac{−27^{3}a^{12}b^{6}}{a^{30}b^{-9}}$
Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$
Hence,
$=\frac{−27^{3}a^{12}b^{6}}{a^{30}b^{-9}}$
$=\frac{−27b^{6+9}}{a^{30-12}}$
$=\frac{−27b^{15}}{a^{18}}$
