Simplify ((15n^5m^3)/(5m^4n^2))^2

${(\frac{15 n^{5} m^{3}}{5 m^{4} n^{2}})}^{2}$

Step 1

Cancel the common factor of $15$ and $5$ .

Factor $5$ out of $15 n^{5} m^{3}$ .

${(\frac{5 (3 n^{5} m^{3})}{5 m^{4} n^{2}})}^{2}$

Cancel the common factors.

Factor $5$ out of $5 m^{4} n^{2}$ .

${(\frac{5 (3 n^{5} m^{3})}{5 (m^{4} n^{2})})}^{2}$

Cancel the common factor.

${(\frac{5 (3 n^{5} m^{3})}{5 (m^{4} n^{2})})}^{2}$

Rewrite the expression.

${(\frac{3 n^{5} m^{3}}{m^{4} n^{2}})}^{2}$

Step 2

Cancel the common factor of $n^{5}$ and $n^{2}$ .

Factor $n^{2}$ out of $3 n^{5} m^{3}$ .

${(\frac{n^{2} (3 n^{3} m^{3})}{m^{4} n^{2}})}^{2}$

Cancel the common factors.

Factor $n^{2}$ out of $m^{4} n^{2}$ .

${(\frac{n^{2} (3 n^{3} m^{3})}{n^{2} m^{4}})}^{2}$

Cancel the common factor.

${(\frac{n^{2} (3 n^{3} m^{3})}{n^{2} m^{4}})}^{2}$

Rewrite the expression.

${(\frac{3 n^{3} m^{3}}{m^{4}})}^{2}$

Step 3

Cancel the common factor of $m^{3}$ and $m^{4}$ .

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

${(\frac{m^{3} (3 n^{3})}{m^{4}})}^{2}$

Cancel the common factors.

Factor $m^{3}$ out of $m^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

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

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

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

Step 5

Simplify the numerator.

Raise $3$ to the power of $2$ .

$\frac{9 {(n^{3})}^{2}}{m^{2}}$

Multiply the exponents in ${(n^{3})}^{2}$ .

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

$\frac{9 n^{3 \cdot 2}}{m^{2}}$

Multiply $3$ by $2$ .

$\frac{9 n^{6}}{m^{2}}$

Simplify ((15n^5m^3)/(5m^4n^2))^2

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