Simplify ((2a^3b^6)/16)^4

${(\frac{2 a^{3} b^{6}}{16})}^{4}$

Cancel the common factor of $2$ and $16$ .

Factor $2$ out of $2 a^{3} b^{6}$ .

${(\frac{2 (a^{3} b^{6})}{16})}^{4}$

Cancel the common factors.

Factor $2$ out of $16$ .

${(\frac{2 (a^{3} b^{6})}{2 \cdot 8})}^{4}$

Cancel the common factor.

${(\frac{2 (a^{3} b^{6})}{2 \cdot 8})}^{4}$

Rewrite the expression.

${(\frac{a^{3} b^{6}}{8})}^{4}$

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

Apply the product rule to $\frac{a^{3} b^{6}}{8}$ .

$\frac{{(a^{3} b^{6})}^{4}}{8^{4}}$

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

$\frac{{(a^{3})}^{4} {(b^{6})}^{4}}{8^{4}}$

Simplify the numerator.

Multiply the exponents in ${(a^{3})}^{4}$ .

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

$\frac{a^{3 \cdot 4} {(b^{6})}^{4}}{8^{4}}$

Multiply $3$ by $4$ .

$\frac{a^{12} {(b^{6})}^{4}}{8^{4}}$

Multiply the exponents in ${(b^{6})}^{4}$ .

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

$\frac{a^{12} b^{6 \cdot 4}}{8^{4}}$

Multiply $6$ by $4$ .

$\frac{a^{12} b^{24}}{8^{4}}$

Raise $8$ to the power of $4$ .

$\frac{a^{12} b^{24}}{4096}$