Simplify ((2r^3t^6)/(5u^9))^4

${(\frac{2 r^{3} t^{6}}{5 u^{9}})}^{4}$

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

Apply the product rule to $\frac{2 r^{3} t^{6}}{5 u^{9}}$ .

$\frac{{(2 r^{3} t^{6})}^{4}}{{(5 u^{9})}^{4}}$

Apply the product rule to $2 r^{3} t^{6}$ .

$\frac{{(2 r^{3})}^{4} {(t^{6})}^{4}}{{(5 u^{9})}^{4}}$

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

$\frac{2^{4} {(r^{3})}^{4} {(t^{6})}^{4}}{{(5 u^{9})}^{4}}$

Apply the product rule to $5 u^{9}$ .

$\frac{2^{4} {(r^{3})}^{4} {(t^{6})}^{4}}{5^{4} {(u^{9})}^{4}}$

Simplify the numerator.

Raise $2$ to the power of $4$ .

$\frac{16 {(r^{3})}^{4} {(t^{6})}^{4}}{5^{4} {(u^{9})}^{4}}$

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

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

$\frac{16 r^{3 \cdot 4} {(t^{6})}^{4}}{5^{4} {(u^{9})}^{4}}$

Multiply $3$ by $4$ .

$\frac{16 r^{12} {(t^{6})}^{4}}{5^{4} {(u^{9})}^{4}}$

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

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

$\frac{16 r^{12} t^{6 \cdot 4}}{5^{4} {(u^{9})}^{4}}$

Multiply $6$ by $4$ .

$\frac{16 r^{12} t^{24}}{5^{4} {(u^{9})}^{4}}$

Simplify the denominator.

Raise $5$ to the power of $4$ .

$\frac{16 r^{12} t^{24}}{625 {(u^{9})}^{4}}$

Multiply the exponents in ${(u^{9})}^{4}$ .

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

$\frac{16 r^{12} t^{24}}{625 u^{9 \cdot 4}}$

Multiply $9$ by $4$ .

$\frac{16 r^{12} t^{24}}{625 u^{36}}$