Simplify (4m^3)/(3m^2n)*(9n^2)/(30m^2n^2)

$\frac{4 m^{3}}{3 m^{2} n} \cdot \frac{9 n^{2}}{30 m^{2} n^{2}}$

Step 1

Combine.

$\frac{4 m^{3} (9 n^{2})}{3 m^{2} n (30 m^{2} n^{2})}$

Step 2

Multiply $m^{2}$ by $m^{2}$ by adding the exponents.

Move $m^{2}$ .

$\frac{4 m^{3} (9 n^{2})}{3 (m^{2} m^{2}) n (30 n^{2})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 m^{3} (9 n^{2})}{3 m^{2 + 2} n (30 n^{2})}$

Add $2$ and $2$ .

$\frac{4 m^{3} (9 n^{2})}{3 m^{4} n (30 n^{2})}$

Step 3

Multiply $n$ by $n^{2}$ by adding the exponents.

Move $n^{2}$ .

$\frac{4 m^{3} (9 n^{2})}{3 m^{4} (n^{2} n) \cdot 30}$

Multiply $n^{2}$ by $n$ .

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

$\frac{4 m^{3} (9 n^{2})}{3 m^{4} (n^{2} n^{1}) \cdot 30}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 m^{3} (9 n^{2})}{3 m^{4} n^{2 + 1} \cdot 30}$

Add $2$ and $1$ .

$\frac{4 m^{3} (9 n^{2})}{3 m^{4} n^{3} \cdot 30}$

Step 4

Cancel the common factor of $4$ and $30$ .

Factor $2$ out of $4 m^{3} (9 n^{2})$ .

$\frac{2 (2 m^{3} (9 n^{2}))}{3 m^{4} n^{3} \cdot 30}$

Cancel the common factors.

Factor $2$ out of $3 m^{4} n^{3} \cdot 30$ .

$\frac{2 (2 m^{3} (9 n^{2}))}{2 (3 m^{4} n^{3} \cdot 15)}$

Cancel the common factor.

$\frac{2 (2 m^{3} (9 n^{2}))}{2 (3 m^{4} n^{3} \cdot 15)}$

Rewrite the expression.

$\frac{2 m^{3} (9 n^{2})}{3 m^{4} n^{3} \cdot 15}$

Step 5

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

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

$\frac{m^{3} (2 (9 n^{2}))}{3 m^{4} n^{3} \cdot 15}$

Cancel the common factors.

Factor $m^{3}$ out of $3 m^{4} n^{3} \cdot 15$ .

$\frac{m^{3} (2 (9 n^{2}))}{m^{3} (3 m n^{3} \cdot 15)}$

Cancel the common factor.

$\frac{m^{3} (2 (9 n^{2}))}{m^{3} (3 m n^{3} \cdot 15)}$

Rewrite the expression.

$\frac{2 (9 n^{2})}{3 m n^{3} \cdot 15}$

Step 6

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $2 (9 n^{2})$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

Cancel the common factor of $3$ and $15$ .

Factor $3$ out of $2 (3 n^{2})$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 8

Cancel the common factor of $n^{2}$ and $n^{3}$ .

Factor $n^{2}$ out of $2 (n^{2})$ .

$\frac{n^{2} \cdot 2}{m n^{3} \cdot 5}$

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{m n \cdot 5}$

Step 9

Move $5$ to the left of $m n$ .

$\frac{2}{5 m n}$

Simplify (4m^3)/(3m^2n)*(9n^2)/(30m^2n^2)

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