Write the Fraction in Simplest Form (12q^-6)/(4(q)^2)

$\frac{12 q^{- 6}}{4 {(q)}^{2}}$

Move $q^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{12}{4 {(q)}^{2} q^{6}}$

Multiply ${(q)}^{2}$ by $q^{6}$ by adding the exponents.

Move $q^{6}$ .

$\frac{12}{4 (q^{6} {(q)}^{2})}$

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

$\frac{12}{4 q^{6 + 2}}$

Add $6$ and $2$ .

$\frac{12}{4 q^{8}}$

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

Factor $4$ out of $12$ .

$\frac{4 \cdot 3}{4 q^{8}}$

Cancel the common factors.

Factor $4$ out of $4 q^{8}$ .

$\frac{4 \cdot 3}{4 (q^{8})}$

Cancel the common factor.

$\frac{4 \cdot 3}{4 q^{8}}$

Rewrite the expression.

$\frac{3}{q^{8}}$