Simplify ((3m^5r^3)/(4p^8))^4

${(\frac{3 m^{5} r^{3}}{4 p^{8}})}^{4}$

Step 1

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

Apply the product rule to $\frac{3 m^{5} r^{3}}{4 p^{8}}$ .

$\frac{{(3 m^{5} r^{3})}^{4}}{{(4 p^{8})}^{4}}$

Apply the product rule to $3 m^{5} r^{3}$ .

$\frac{{(3 m^{5})}^{4} {(r^{3})}^{4}}{{(4 p^{8})}^{4}}$

Apply the product rule to $3 m^{5}$ .

$\frac{3^{4} {(m^{5})}^{4} {(r^{3})}^{4}}{{(4 p^{8})}^{4}}$

Apply the product rule to $4 p^{8}$ .

$\frac{3^{4} {(m^{5})}^{4} {(r^{3})}^{4}}{4^{4} {(p^{8})}^{4}}$

Step 2

Simplify the numerator.

Raise $3$ to the power of $4$ .

$\frac{81 {(m^{5})}^{4} {(r^{3})}^{4}}{4^{4} {(p^{8})}^{4}}$

Multiply the exponents in ${(m^{5})}^{4}$ .

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

$\frac{81 m^{5 \cdot 4} {(r^{3})}^{4}}{4^{4} {(p^{8})}^{4}}$

Multiply $5$ by $4$ .

$\frac{81 m^{20} {(r^{3})}^{4}}{4^{4} {(p^{8})}^{4}}$

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

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

$\frac{81 m^{20} r^{3 \cdot 4}}{4^{4} {(p^{8})}^{4}}$

Multiply $3$ by $4$ .

$\frac{81 m^{20} r^{12}}{4^{4} {(p^{8})}^{4}}$

Step 3

Simplify the denominator.

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

$\frac{81 m^{20} r^{12}}{256 {(p^{8})}^{4}}$

Multiply the exponents in ${(p^{8})}^{4}$ .

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

$\frac{81 m^{20} r^{12}}{256 p^{8 \cdot 4}}$

Multiply $8$ by $4$ .

$\frac{81 m^{20} r^{12}}{256 p^{32}}$