Simplify 1/2q^4(4mn)q^-5

$\frac{1}{2} q^{4} (4 m n) q^{- 5}$

Multiply $q^{4}$ by $q^{- 5}$ by adding the exponents.

Move $q^{- 5}$ .

$\frac{1}{2} \cdot (q^{- 5} q^{4} (4 m n))$

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

$\frac{1}{2} \cdot (q^{- 5 + 4} (4 m n))$

Add $- 5$ and $4$ .

$\frac{1}{2} \cdot (q^{- 1} (4 m n))$

Cancel the common factor of $2$ .

Factor $2$ out of $q^{- 1} (4 m n)$ .

$\frac{1}{2} \cdot (2 (q^{- 1} (2 m n)))$

Cancel the common factor.

$\frac{1}{2} \cdot (2 (q^{- 1} (2 m n)))$

Rewrite the expression.

$q^{- 1} (2 m n)$

Rewrite using the commutative property of multiplication.

$2 q^{- 1} m n$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 \frac{1}{q} m n$

Combine $2$ and $\frac{1}{q}$ .

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

Combine $\frac{2}{q}$ and $m$ .

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

Combine $\frac{2 m}{q}$ and $n$ .

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