Write the Fraction in Simplest Form ((-3q^-3)^3)/(-6q^-6)

$\frac{{(- 3 q^{- 3})}^{3}}{- 6 q^{- 6}}$

Step 1

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

$\frac{{(- 3 q^{- 3})}^{3} q^{6}}{- 6}$

Step 2

Simplify the numerator.

Apply the product rule to $- 3 q^{- 3}$ .

$\frac{{(- 3)}^{3} {(q^{- 3})}^{3} q^{6}}{- 6}$

Raise $- 3$ to the power of $3$ .

$\frac{- 27 {(q^{- 3})}^{3} q^{6}}{- 6}$

Multiply the exponents in ${(q^{- 3})}^{3}$ .

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

$\frac{- 27 q^{- 3 \cdot 3} q^{6}}{- 6}$

Multiply $- 3$ by $3$ .

$\frac{- 27 q^{- 9} q^{6}}{- 6}$

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

$\frac{- 27 \frac{1}{q^{9}} q^{6}}{- 6}$

Combine exponents.

Combine $- 27$ and $\frac{1}{q^{9}}$ .

$\frac{\frac{- 27}{q^{9}} q^{6}}{- 6}$

Combine $\frac{- 27}{q^{9}}$ and $q^{6}$ .

$\frac{\frac{- 27 q^{6}}{q^{9}}}{- 6}$

Reduce the expression $\frac{- 27 q^{6}}{q^{9}}$ by cancelling the common factors.

Factor $q^{6}$ out of $- 27 q^{6}$ .

$\frac{\frac{q^{6} \cdot - 27}{q^{9}}}{- 6}$

Factor $q^{6}$ out of $q^{9}$ .

$\frac{\frac{q^{6} \cdot - 27}{q^{6} q^{3}}}{- 6}$

Cancel the common factor.

$\frac{\frac{q^{6} \cdot - 27}{q^{6} q^{3}}}{- 6}$

Rewrite the expression.

$\frac{\frac{- 27}{q^{3}}}{- 6}$

Move the negative in front of the fraction.

$\frac{- \frac{27}{q^{3}}}{- 6}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{27}{q^{3}} \cdot \frac{1}{- 6}$

Step 4

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{27}{q^{3}}$ into the numerator.

$\frac{- 27}{q^{3}} \cdot \frac{1}{- 6}$

Factor $3$ out of $- 27$ .

$\frac{3 (- 9)}{q^{3}} \cdot \frac{1}{- 6}$

Factor $3$ out of $- 6$ .

$\frac{3 \cdot - 9}{q^{3}} \cdot \frac{1}{3 \cdot - 2}$

Cancel the common factor.

$\frac{3 \cdot - 9}{q^{3}} \cdot \frac{1}{3 \cdot - 2}$

Rewrite the expression.

$\frac{- 9}{q^{3}} \cdot \frac{1}{- 2}$

Step 5

Multiply $\frac{- 9}{q^{3}}$ by $\frac{1}{- 2}$ .

$\frac{- 9}{q^{3} \cdot - 2}$

Step 6

Move $- 2$ to the left of $q^{3}$ .

$\frac{- 9}{- 2 \cdot q^{3}}$

Step 7

Dividing two negative values results in a positive value.

$\frac{9}{2 q^{3}}$

Write the Fraction in Simplest Form ((-3q^-3)^3)/(-6q^-6)

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