Simplify ((3m^4n)^3(2m^2n^5p))/(6m^4n^9p^8)

$\frac{{(3 m^{4} n)}^{3} (2 m^{2} n^{5} p)}{6 m^{4} n^{9} p^{8}}$

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of ${(3 m^{4} n)}^{3} (2 m^{2} n^{5} p)$ .

$\frac{2 ({(3 m^{4} n)}^{3} (m^{2} n^{5} p))}{6 m^{4} n^{9} p^{8}}$

Cancel the common factors.

Factor $2$ out of $6 m^{4} n^{9} p^{8}$ .

$\frac{2 ({(3 m^{4} n)}^{3} (m^{2} n^{5} p))}{2 (3 m^{4} n^{9} p^{8})}$

Cancel the common factor.

$\frac{2 ({(3 m^{4} n)}^{3} (m^{2} n^{5} p))}{2 (3 m^{4} n^{9} p^{8})}$

Rewrite the expression.

$\frac{{(3 m^{4} n)}^{3} (m^{2} n^{5} p)}{3 m^{4} n^{9} p^{8}}$

Cancel the common factor of $m^{2}$ and $m^{4}$ .

Factor $m^{2}$ out of ${(3 m^{4} n)}^{3} (m^{2} n^{5} p)$ .

$\frac{m^{2} ({(3 m^{4} n)}^{3} (n^{5} p))}{3 m^{4} n^{9} p^{8}}$

Cancel the common factors.

Factor $m^{2}$ out of $3 m^{4} n^{9} p^{8}$ .

$\frac{m^{2} ({(3 m^{4} n)}^{3} (n^{5} p))}{m^{2} (3 m^{2} n^{9} p^{8})}$

Cancel the common factor.

$\frac{m^{2} ({(3 m^{4} n)}^{3} (n^{5} p))}{m^{2} (3 m^{2} n^{9} p^{8})}$

Rewrite the expression.

$\frac{{(3 m^{4} n)}^{3} (n^{5} p)}{3 m^{2} n^{9} p^{8}}$

Cancel the common factor of $n^{5}$ and $n^{9}$ .

Factor $n^{5}$ out of ${(3 m^{4} n)}^{3} (n^{5} p)$ .

$\frac{n^{5} ({(3 m^{4} n)}^{3} (p))}{3 m^{2} n^{9} p^{8}}$

Cancel the common factors.

Factor $n^{5}$ out of $3 m^{2} n^{9} p^{8}$ .

$\frac{n^{5} ({(3 m^{4} n)}^{3} (p))}{n^{5} (3 m^{2} n^{4} p^{8})}$

Cancel the common factor.

$\frac{n^{5} ({(3 m^{4} n)}^{3} (p))}{n^{5} (3 m^{2} n^{4} p^{8})}$

Rewrite the expression.

$\frac{{(3 m^{4} n)}^{3} (p)}{3 m^{2} n^{4} p^{8}}$

Cancel the common factor of $p$ and $p^{8}$ .

Factor $p$ out of ${(3 m^{4} n)}^{3} (p)$ .

$\frac{p {(3 m^{4} n)}^{3}}{3 m^{2} n^{4} p^{8}}$

Cancel the common factors.

Factor $p$ out of $3 m^{2} n^{4} p^{8}$ .

$\frac{p {(3 m^{4} n)}^{3}}{p (3 m^{2} n^{4} p^{7})}$

Cancel the common factor.

$\frac{p {(3 m^{4} n)}^{3}}{p (3 m^{2} n^{4} p^{7})}$

Rewrite the expression.

$\frac{{(3 m^{4} n)}^{3}}{3 m^{2} n^{4} p^{7}}$

Step 2

Simplify the numerator.

Apply the product rule to $3 m^{4} n$ .

$\frac{{(3 m^{4})}^{3} n^{3}}{3 m^{2} n^{4} p^{7}}$

Apply the product rule to $3 m^{4}$ .

$\frac{3^{3} {(m^{4})}^{3} n^{3}}{3 m^{2} n^{4} p^{7}}$

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

$\frac{27 {(m^{4})}^{3} n^{3}}{3 m^{2} n^{4} p^{7}}$

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

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

$\frac{27 m^{4 \cdot 3} n^{3}}{3 m^{2} n^{4} p^{7}}$

Multiply $4$ by $3$ .

$\frac{27 m^{12} n^{3}}{3 m^{2} n^{4} p^{7}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $27$ and $3$ .

Factor $3$ out of $27 m^{12} n^{3}$ .

$\frac{3 (9 m^{12} n^{3})}{3 m^{2} n^{4} p^{7}}$

Cancel the common factors.

Factor $3$ out of $3 m^{2} n^{4} p^{7}$ .

$\frac{3 (9 m^{12} n^{3})}{3 (m^{2} n^{4} p^{7})}$

Cancel the common factor.

$\frac{3 (9 m^{12} n^{3})}{3 (m^{2} n^{4} p^{7})}$

Rewrite the expression.

$\frac{9 m^{12} n^{3}}{m^{2} n^{4} p^{7}}$

Cancel the common factor of $m^{12}$ and $m^{2}$ .

Factor $m^{2}$ out of $9 m^{12} n^{3}$ .

$\frac{m^{2} (9 m^{10} n^{3})}{m^{2} n^{4} p^{7}}$

Cancel the common factors.

Factor $m^{2}$ out of $m^{2} n^{4} p^{7}$ .

$\frac{m^{2} (9 m^{10} n^{3})}{m^{2} (n^{4} p^{7})}$

Cancel the common factor.

$\frac{m^{2} (9 m^{10} n^{3})}{m^{2} (n^{4} p^{7})}$

Rewrite the expression.

$\frac{9 m^{10} n^{3}}{n^{4} p^{7}}$

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

Factor $n^{3}$ out of $9 m^{10} n^{3}$ .

$\frac{n^{3} (9 m^{10})}{n^{4} p^{7}}$

Cancel the common factors.

Factor $n^{3}$ out of $n^{4} p^{7}$ .

$\frac{n^{3} (9 m^{10})}{n^{3} (n p^{7})}$

Cancel the common factor.

$\frac{n^{3} (9 m^{10})}{n^{3} (n p^{7})}$

Rewrite the expression.

$\frac{9 m^{10}}{n p^{7}}$

Simplify ((3m^4n)^3(2m^2n^5p))/(6m^4n^9p^8)

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