Simplify (12y^5m)/(4(y^3m^4)^-2)

$\frac{12 y^{5} m}{4 {(y^{3} m^{4})}^{- 2}}$

Move ${(y^{3} m^{4})}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{12 y^{5} m {(y^{3} m^{4})}^{2}}{4}$

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12 y^{5} m {(y^{3} m^{4})}^{2}$ .

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

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{4 (3 y^{5} m {(y^{3} m^{4})}^{2})}{4 (1)}$

Cancel the common factor.

$\frac{4 (3 y^{5} m {(y^{3} m^{4})}^{2})}{4 \cdot 1}$

Rewrite the expression.

$\frac{3 y^{5} m {(y^{3} m^{4})}^{2}}{1}$

Divide $3 y^{5} m {(y^{3} m^{4})}^{2}$ by $1$ .

$3 y^{5} m {(y^{3} m^{4})}^{2}$

Apply basic rules of exponents.

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

$3 y^{5} m ({(y^{3})}^{2} {(m^{4})}^{2})$

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

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

$3 y^{5} m (y^{3 \cdot 2} {(m^{4})}^{2})$

Multiply $3$ by $2$ .

$3 y^{5} m (y^{6} {(m^{4})}^{2})$

Multiply $y^{5}$ by $y^{6}$ by adding the exponents.

Move $y^{6}$ .

$3 (y^{6} y^{5}) m {(m^{4})}^{2}$

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

$3 y^{6 + 5} m {(m^{4})}^{2}$

Add $6$ and $5$ .

$3 y^{11} m {(m^{4})}^{2}$

Multiply the exponents in ${(m^{4})}^{2}$ .

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

$3 y^{11} m \cdot m^{4 \cdot 2}$

Multiply $4$ by $2$ .

$3 y^{11} m \cdot m^{8}$

Multiply $m$ by $m^{8}$ by adding the exponents.

Move $m^{8}$ .

$3 y^{11} (m^{8} m)$

Multiply $m^{8}$ by $m$ .

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

$3 y^{11} (m^{8} m^{1})$

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

$3 y^{11} m^{8 + 1}$

Add $8$ and $1$ .

$3 y^{11} m^{9}$