Simplify ((2a^3b^-2)/(c^3))^5

${(\frac{2 a^{3} b^{- 2}}{c^{3}})}^{5}$

Move $b^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{2 a^{3}}{c^{3} b^{2}})}^{5}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 a^{3}}{c^{3} b^{2}}$ .

$\frac{{(2 a^{3})}^{5}}{{(c^{3} b^{2})}^{5}}$

Apply the product rule to $2 a^{3}$ .

$\frac{2^{5} {(a^{3})}^{5}}{{(c^{3} b^{2})}^{5}}$

Apply the product rule to $c^{3} b^{2}$ .

$\frac{2^{5} {(a^{3})}^{5}}{{(c^{3})}^{5} {(b^{2})}^{5}}$

Simplify the numerator.

Raise $2$ to the power of $5$ .

$\frac{32 {(a^{3})}^{5}}{{(c^{3})}^{5} {(b^{2})}^{5}}$

Multiply the exponents in ${(a^{3})}^{5}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{32 a^{3 \cdot 5}}{{(c^{3})}^{5} {(b^{2})}^{5}}$

Multiply $3$ by $5$ .

$\frac{32 a^{15}}{{(c^{3})}^{5} {(b^{2})}^{5}}$

Simplify the denominator.

Multiply the exponents in ${(c^{3})}^{5}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{32 a^{15}}{c^{3 \cdot 5} {(b^{2})}^{5}}$

Multiply $3$ by $5$ .

$\frac{32 a^{15}}{c^{15} {(b^{2})}^{5}}$

Multiply the exponents in ${(b^{2})}^{5}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{32 a^{15}}{c^{15} b^{2 \cdot 5}}$

Multiply $2$ by $5$ .

$\frac{32 a^{15}}{c^{15} b^{10}}$