Basic Math Examples

${(- 3)}^{3} \cdot {(- 4)}^{5} \cdot {(- 6)}^{3} \div 6^{6}$

Step 1

Rewrite the division as a fraction.

$\frac{{(- 3)}^{3} \cdot {(- 4)}^{5} \cdot {(- 6)}^{3}}{6^{6}}$

Step 2

Cancel the common factor of ${(- 6)}^{3}$ and $6^{6}$ .

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Step 2.1

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{{(- 3)}^{3} \cdot {(- 4)}^{5} \cdot {(- 1 (6))}^{3}}{6^{6}}$

Step 2.2

Apply the product rule to $- 1 (6)$ .

$\frac{{(- 3)}^{3} \cdot {(- 4)}^{5} \cdot ({(- 1)}^{3} \cdot 6^{3})}{6^{6}}$

Step 2.3

Raise $- 1$ to the power of $3$ .

$\frac{{(- 3)}^{3} \cdot {(- 4)}^{5} \cdot (- 1 \cdot 6^{3})}{6^{6}}$

Step 2.4

Factor $6^{3}$ out of ${(- 3)}^{3} \cdot {(- 4)}^{5} \cdot - 1 \cdot 6^{3}$ .

$\frac{6^{3} \cdot ({(- 3)}^{3} \cdot {(- 4)}^{5} \cdot - 1)}{6^{6}}$

Step 2.5

Cancel the common factors.

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Step 2.5.1

Factor $6^{3}$ out of $6^{6}$ .

$\frac{6^{3} \cdot ({(- 3)}^{3} \cdot {(- 4)}^{5} \cdot - 1)}{6^{3} \cdot 6^{3}}$

Step 2.5.2

Cancel the common factor.

$\frac{6^{3} \cdot ({(- 3)}^{3} \cdot {(- 4)}^{5} \cdot - 1)}{6^{3} \cdot 6^{3}}$

Step 2.5.3

Rewrite the expression.

$\frac{{(- 3)}^{3} \cdot {(- 4)}^{5} \cdot - 1}{6^{3}}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{- 27 \cdot {(- 4)}^{5} \cdot - 1}{6^{3}}$

Step 3.2

Raise $- 4$ to the power of $5$ .

$\frac{- 27 \cdot - 1024 \cdot - 1}{6^{3}}$

Step 3.3

Combine exponents.

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Step 3.3.1

Multiply $- 27$ by $- 1024$ .

$\frac{27648 \cdot - 1}{6^{3}}$

Step 3.3.2

Multiply $27648$ by $- 1$ .

$\frac{- 27648}{6^{3}}$

Step 4

Simplify the expression.

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Step 4.1

Raise $6$ to the power of $3$ .

$\frac{- 27648}{216}$

Step 4.2

Divide $- 27648$ by $216$ .

$- 128$