Pre-Algebra Examples

$- 27 x^{6} y^{- 3} \cdot \frac{2}{3}$

Step 1

Cancel the common factor of $3$ .

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Step 1.1

Factor $3$ out of $- 27 x^{6} y^{- 3}$ .

$3 (- 9 x^{6} y^{- 3}) \cdot \frac{2}{3}$

Step 1.2

Cancel the common factor.

$3 (- 9 x^{6} y^{- 3}) \cdot \frac{2}{3}$

Step 1.3

Rewrite the expression.

$- 9 x^{6} y^{- 3} \cdot 2$

Step 2

Multiply $2$ by $- 9$ .

$- 18 x^{6} y^{- 3}$

Step 3

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

$- 18 x^{6} \frac{1}{y^{3}}$

Step 4

Multiply $- 18 x^{6} \frac{1}{y^{3}}$ .

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Step 4.1

Combine $- 18$ and $\frac{1}{y^{3}}$ .

$x^{6} \frac{- 18}{y^{3}}$

Step 4.2

Combine $x^{6}$ and $\frac{- 18}{y^{3}}$ .

$\frac{x^{6} \cdot - 18}{y^{3}}$

Step 5

Move $- 18$ to the left of $x^{6}$ .

$\frac{- 18 \cdot x^{6}}{y^{3}}$

Step 6

Move the negative in front of the fraction.

$- \frac{18 x^{6}}{y^{3}}$