Simplify (12m^5w^6)/(3w^4)*(5(m^4)^3)/(w^-3)

$\frac{12 m^{5} w^{6}}{3 w^{4}} \cdot \frac{5 {(m^{4})}^{3}}{w^{- 3}}$

Step 1

Combine.

$\frac{12 m^{5} w^{6} (5 {(m^{4})}^{3})}{3 w^{4} w^{- 3}}$

Step 2

Multiply $w^{4}$ by $w^{- 3}$ by adding the exponents.

Move $w^{- 3}$ .

$\frac{12 m^{5} w^{6} (5 {(m^{4})}^{3})}{3 (w^{- 3} w^{4})}$

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

$\frac{12 m^{5} w^{6} (5 {(m^{4})}^{3})}{3 w^{- 3 + 4}}$

Add $- 3$ and $4$ .

$\frac{12 m^{5} w^{6} (5 {(m^{4})}^{3})}{3 w^{1}}$

Step 3

Simplify $3 w^{1}$ .

$\frac{12 m^{5} w^{6} (5 {(m^{4})}^{3})}{3 w}$

Step 4

Cancel the common factor of $12$ and $3$ .

Factor $3$ out of $12 m^{5} w^{6} (5 {(m^{4})}^{3})$ .

$\frac{3 (4 m^{5} w^{6} (5 {(m^{4})}^{3}))}{3 w}$

Cancel the common factors.

Factor $3$ out of $3 w$ .

$\frac{3 (4 m^{5} w^{6} (5 {(m^{4})}^{3}))}{3 (w)}$

Cancel the common factor.

$\frac{3 (4 m^{5} w^{6} (5 {(m^{4})}^{3}))}{3 w}$

Rewrite the expression.

$\frac{4 m^{5} w^{6} (5 {(m^{4})}^{3})}{w}$

Step 5

Cancel the common factor of $w^{6}$ and $w$ .

Factor $w$ out of $4 m^{5} w^{6} (5 {(m^{4})}^{3})$ .

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

Cancel the common factors.

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

$\frac{w (4 m^{5} w^{5} (5 {(m^{4})}^{3}))}{w^{1}}$

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

$\frac{w (4 m^{5} w^{5} (5 {(m^{4})}^{3}))}{w \cdot 1}$

Cancel the common factor.

$\frac{w (4 m^{5} w^{5} (5 {(m^{4})}^{3}))}{w \cdot 1}$

Rewrite the expression.

$\frac{4 m^{5} w^{5} (5 {(m^{4})}^{3})}{1}$

Divide $4 m^{5} w^{5} (5 {(m^{4})}^{3})$ by $1$ .

$4 m^{5} w^{5} (5 {(m^{4})}^{3})$

Step 6

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

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

$4 m^{5} w^{5} (5 m^{4 \cdot 3})$

Multiply $4$ by $3$ .

$4 m^{5} w^{5} (5 m^{12})$

Step 7

Multiply $m^{5}$ by $m^{12}$ by adding the exponents.

Move $m^{12}$ .

$4 (m^{12} m^{5}) w^{5} \cdot 5$

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

$4 m^{12 + 5} w^{5} \cdot 5$

Add $12$ and $5$ .

$4 m^{17} w^{5} \cdot 5$

Step 8

Multiply $5$ by $4$ .

$20 m^{17} w^{5}$

Simplify (12m^5w^6)/(3w^4)*(5(m^4)^3)/(w^-3)

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