Simplify ((a^8b^6)/(a^11))^5

${(\frac{a^{8} b^{6}}{a^{11}})}^{5}$

Cancel the common factor of $a^{8}$ and $a^{11}$ .

Factor $a^{8}$ out of $a^{8} b^{6}$ .

${(\frac{a^{8} (b^{6})}{a^{11}})}^{5}$

Cancel the common factors.

Factor $a^{8}$ out of $a^{11}$ .

${(\frac{a^{8} (b^{6})}{a^{8} a^{3}})}^{5}$

Cancel the common factor.

${(\frac{a^{8} b^{6}}{a^{8} a^{3}})}^{5}$

Rewrite the expression.

${(\frac{b^{6}}{a^{3}})}^{5}$

Apply basic rules of exponents.

Apply the product rule to $\frac{b^{6}}{a^{3}}$ .

$\frac{{(b^{6})}^{5}}{{(a^{3})}^{5}}$

Multiply the exponents in ${(b^{6})}^{5}$ .

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

$\frac{b^{6 \cdot 5}}{{(a^{3})}^{5}}$

Multiply $6$ by $5$ .

$\frac{b^{30}}{{(a^{3})}^{5}}$

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

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

$\frac{b^{30}}{a^{3 \cdot 5}}$

Multiply $3$ by $5$ .

$\frac{b^{30}}{a^{15}}$