## Algebra: A Combined Approach (4th Edition)

$\Big(\dfrac{a^{5}bc^{0}}{a^{7}b^{-2}}\Big)^{-3}=\dfrac{a^{6}}{b^{9}}$
$\Big(\dfrac{a^{5}bc^{0}}{a^{7}b^{-2}}\Big)^{-3}$ First, we know that $c^{0}=1$. So, this expression can be rewritten as: $\Big(\dfrac{a^{5}bc^{0}}{a^{7}b^{-2}}\Big)^{-3}=\Big(\dfrac{a^{5}b}{a^{7}b^{-2}}\Big)^{-3}=...$ To change the exponent's sign, write the denominator as the numerator and vice versa: $...=\Big(\dfrac{a^{7}b^{-2}}{a^{5}b}\Big)^{3}=...$ Evaluate the exponential expression: $...=\dfrac{a^{21}b^{-6}}{a^{15}b^{3}}=...$ Finally, perform the division and simplify: $...=a^{21-15}b^{-6-3}=a^{6}b^{-9}=\dfrac{a^{6}}{b^{9}}$