Simplify ((3m^2n^7)/m)^5

${(\frac{3 m^{2} n^{7}}{m})}^{5}$

Step 1

Cancel the common factor of $m^{2}$ and $m$ .

Factor $m$ out of $3 m^{2} n^{7}$ .

${(\frac{m (3 m n^{7})}{m})}^{5}$

Cancel the common factors.

Raise $m$ to the power of $1$ .

${(\frac{m (3 m n^{7})}{m^{1}})}^{5}$

Factor $m$ out of $m^{1}$ .

${(\frac{m (3 m n^{7})}{m \cdot 1})}^{5}$

Cancel the common factor.

${(\frac{m (3 m n^{7})}{m \cdot 1})}^{5}$

Rewrite the expression.

${(\frac{3 m n^{7}}{1})}^{5}$

Divide $3 m n^{7}$ by $1$ .

${(3 m n^{7})}^{5}$

Step 2

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

Apply the product rule to $3 m n^{7}$ .

${(3 m)}^{5} {(n^{7})}^{5}$

Apply the product rule to $3 m$ .

$3^{5} m^{5} {(n^{7})}^{5}$

Step 3

Raise $3$ to the power of $5$ .

$243 m^{5} {(n^{7})}^{5}$

Step 4

Multiply the exponents in ${(n^{7})}^{5}$ .

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

$243 m^{5} n^{7 \cdot 5}$

Multiply $7$ by $5$ .

$243 m^{5} n^{35}$