Basic Math Examples

${(5 - 7)}^{3} - 5 + 2 \cdot 3^{3} \div 9 + 15$

Step 1

Find the common denominator.

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Step 1.1

Write ${(5 - 7)}^{3}$ as a fraction with denominator $1$ .

$\frac{{(5 - 7)}^{3}}{1} - 5 + 2 \cdot 3^{3} \div 9 + 15$

Step 1.2

Multiply $\frac{{(5 - 7)}^{3}}{1}$ by $\frac{9}{9}$ .

$\frac{{(5 - 7)}^{3}}{1} \cdot \frac{9}{9} - 5 + 2 \cdot 3^{3} \div 9 + 15$

Step 1.3

Multiply $\frac{{(5 - 7)}^{3}}{1}$ by $\frac{9}{9}$ .

$\frac{{(5 - 7)}^{3} \cdot 9}{9} - 5 + 2 \cdot 3^{3} \div 9 + 15$

Step 1.4

Write $- 5$ as a fraction with denominator $1$ .

$\frac{{(5 - 7)}^{3} \cdot 9}{9} + \frac{- 5}{1} + 2 \cdot 3^{3} \div 9 + 15$

Step 1.5

Multiply $\frac{- 5}{1}$ by $\frac{9}{9}$ .

$\frac{{(5 - 7)}^{3} \cdot 9}{9} + \frac{- 5}{1} \cdot \frac{9}{9} + 2 \cdot 3^{3} \div 9 + 15$

Step 1.6

Multiply $\frac{- 5}{1}$ by $\frac{9}{9}$ .

$\frac{{(5 - 7)}^{3} \cdot 9}{9} + \frac{- 5 \cdot 9}{9} + 2 \cdot 3^{3} \div 9 + 15$

Step 1.7

Write $15$ as a fraction with denominator $1$ .

$\frac{{(5 - 7)}^{3} \cdot 9}{9} + \frac{- 5 \cdot 9}{9} + 2 \cdot 3^{3} \div 9 + \frac{15}{1}$

Step 1.8

Multiply $\frac{15}{1}$ by $\frac{9}{9}$ .

$\frac{{(5 - 7)}^{3} \cdot 9}{9} + \frac{- 5 \cdot 9}{9} + 2 \cdot 3^{3} \div 9 + \frac{15}{1} \cdot \frac{9}{9}$

Step 1.9

Multiply $\frac{15}{1}$ by $\frac{9}{9}$ .

$\frac{{(5 - 7)}^{3} \cdot 9}{9} + \frac{- 5 \cdot 9}{9} + 2 \cdot 3^{3} \div 9 + \frac{15 \cdot 9}{9}$

Step 2

Combine the numerators over the common denominator.

$\frac{{(5 - 7)}^{3} \cdot 9 - 5 \cdot 9 + 2 \cdot 3^{3} + 15 \cdot 9}{9}$

Step 3

Simplify each term.

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Step 3.1

Subtract $7$ from $5$ .

$\frac{{(- 2)}^{3} \cdot 9 - 5 \cdot 9 + 2 \cdot 3^{3} + 15 \cdot 9}{9}$

Step 3.2

Raise $- 2$ to the power of $3$ .

$\frac{- 8 \cdot 9 - 5 \cdot 9 + 2 \cdot 3^{3} + 15 \cdot 9}{9}$

Step 3.3

Multiply $- 8$ by $9$ .

$\frac{- 72 - 5 \cdot 9 + 2 \cdot 3^{3} + 15 \cdot 9}{9}$

Step 3.4

Multiply $- 5$ by $9$ .

$\frac{- 72 - 45 + 2 \cdot 3^{3} + 15 \cdot 9}{9}$

Step 3.5

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

$\frac{- 72 - 45 + 2 \cdot 27 + 15 \cdot 9}{9}$

Step 3.6

Multiply $2$ by $27$ .

$\frac{- 72 - 45 + 54 + 15 \cdot 9}{9}$

Step 3.7

Multiply $15$ by $9$ .

$\frac{- 72 - 45 + 54 + 135}{9}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $45$ from $- 72$ .

$\frac{- 117 + 54 + 135}{9}$

Step 4.2

Add $- 117$ and $54$ .

$\frac{- 63 + 135}{9}$

Step 4.3

Add $- 63$ and $135$ .

$\frac{72}{9}$

Step 4.4

Divide $72$ by $9$ .

$8$