Basic Math Examples

$\frac{162 (- \frac{4}{3^{3}} - 1)}{- \frac{4}{3 - 1}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$162 (- \frac{4}{3^{3}} - 1) (- \frac{3 - 1}{4})$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Move the leading negative in $- \frac{3 - 1}{4}$ into the numerator.

$162 (- \frac{4}{3^{3}} - 1) \frac{- (3 - 1)}{4}$

Step 2.2

Factor $2$ out of $162 (- \frac{4}{3^{3}} - 1)$ .

$2 (81 (- \frac{4}{3^{3}} - 1)) \frac{- (3 - 1)}{4}$

Step 2.3

Factor $2$ out of $4$ .

$2 (81 (- \frac{4}{3^{3}} - 1)) \frac{- (3 - 1)}{2 (2)}$

Step 2.4

Cancel the common factor.

$2 (81 (- \frac{4}{3^{3}} - 1)) \frac{- (3 - 1)}{2 \cdot 2}$

Step 2.5

Rewrite the expression.

$81 (- \frac{4}{3^{3}} - 1) \frac{- (3 - 1)}{2}$

Step 3

Combine $\frac{- (3 - 1)}{2}$ and $81$ .

$\frac{- (3 - 1) \cdot 81}{2} (- \frac{4}{3^{3}} - 1)$

Step 4

Simplify the expression.

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Step 4.1

Multiply $81$ by $- 1$ .

$\frac{- 81 (3 - 1)}{2} (- \frac{4}{3^{3}} - 1)$

Step 4.2

Subtract $1$ from $3$ .

$\frac{- 81 \cdot 2}{2} (- \frac{4}{3^{3}} - 1)$

Step 4.3

Multiply $- 81$ by $2$ .

$\frac{- 162}{2} (- \frac{4}{3^{3}} - 1)$

Step 4.4

Divide $- 162$ by $2$ .

$- 81 (- \frac{4}{3^{3}} - 1)$

Step 4.5

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

$- 81 (- \frac{4}{27} - 1)$

Step 5

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$- 81 (- \frac{4}{27} - 1 \cdot \frac{27}{27})$

Step 6

Combine $- 1$ and $\frac{27}{27}$ .

$- 81 (- \frac{4}{27} + \frac{- 1 \cdot 27}{27})$

Step 7

Combine the numerators over the common denominator.

$- 81 \frac{- 4 - 1 \cdot 27}{27}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $- 1$ by $27$ .

$- 81 \frac{- 4 - 27}{27}$

Step 8.2

Subtract $27$ from $- 4$ .

$- 81 (\frac{- 31}{27})$

Step 9

Cancel the common factor of $27$ .

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Step 9.1

Factor $27$ out of $- 81$ .

$27 (- 3) \frac{- 31}{27}$

Step 9.2

Cancel the common factor.

$27 \cdot - 3 \frac{- 31}{27}$

Step 9.3

Rewrite the expression.

$- 3 \cdot - 31$

Step 10

Multiply $- 3$ by $- 31$ .

$93$