Answer
$\Big(\dfrac{a^{5}bc^{0}}{a^{7}b^{-2}}\Big)^{-3}=\dfrac{a^{6}}{b^{9}}$
Work Step by Step
$\Big(\dfrac{a^{5}bc^{0}}{a^{7}b^{-2}}\Big)^{-3}$
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:
$...=a^{21-15}b^{-6-3}=a^{6}b^{-9}=\dfrac{a^{6}}{b^{9}}$
