Basic Math Examples

$- 5^{2} + 138 \div 6 - {(4 + 2)}^{3}$

Step 1

Find the common denominator.

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Step 1.1

Write $- 5^{2}$ as a fraction with denominator $1$ .

$\frac{- 5^{2}}{1} + 138 \div 6 - {(4 + 2)}^{3}$

Step 1.2

Multiply $\frac{- 5^{2}}{1}$ by $\frac{6}{6}$ .

$\frac{- 5^{2}}{1} \cdot \frac{6}{6} + 138 \div 6 - {(4 + 2)}^{3}$

Step 1.3

Multiply $\frac{- 5^{2}}{1}$ by $\frac{6}{6}$ .

$\frac{- 5^{2} \cdot 6}{6} + 138 \div 6 - {(4 + 2)}^{3}$

Step 1.4

Write $- {(4 + 2)}^{3}$ as a fraction with denominator $1$ .

$\frac{- 5^{2} \cdot 6}{6} + 138 \div 6 + \frac{- {(4 + 2)}^{3}}{1}$

Step 1.5

Multiply $\frac{- {(4 + 2)}^{3}}{1}$ by $\frac{6}{6}$ .

$\frac{- 5^{2} \cdot 6}{6} + 138 \div 6 + \frac{- {(4 + 2)}^{3}}{1} \cdot \frac{6}{6}$

Step 1.6

Multiply $\frac{- {(4 + 2)}^{3}}{1}$ by $\frac{6}{6}$ .

$\frac{- 5^{2} \cdot 6}{6} + 138 \div 6 + \frac{- {(4 + 2)}^{3} \cdot 6}{6}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 5^{2} \cdot 6 + 138 - {(4 + 2)}^{3} \cdot 6}{6}$

Step 3

Simplify each term.

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Step 3.1

Raise $5$ to the power of $2$ .

$\frac{- 1 \cdot 25 \cdot 6 + 138 - {(4 + 2)}^{3} \cdot 6}{6}$

Step 3.2

Multiply $- 1 \cdot 25 \cdot 6$ .

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Step 3.2.1

Multiply $- 1$ by $25$ .

$\frac{- 25 \cdot 6 + 138 - {(4 + 2)}^{3} \cdot 6}{6}$

Step 3.2.2

Multiply $- 25$ by $6$ .

$\frac{- 150 + 138 - {(4 + 2)}^{3} \cdot 6}{6}$

Step 3.3

Add $4$ and $2$ .

$\frac{- 150 + 138 - 6^{3} \cdot 6}{6}$

Step 3.4

Multiply $6^{3}$ by $6$ by adding the exponents.

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Step 3.4.1

Move $6$ .

$\frac{- 150 + 138 - (6 \cdot 6^{3})}{6}$

Step 3.4.2

Multiply $6$ by $6^{3}$ .

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Step 3.4.2.1

Raise $6$ to the power of $1$ .

$\frac{- 150 + 138 - (6^{1} \cdot 6^{3})}{6}$

Step 3.4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 150 + 138 - 6^{1 + 3}}{6}$

Step 3.4.3

Add $1$ and $3$ .

$\frac{- 150 + 138 - 6^{4}}{6}$

Step 3.5

Raise $6$ to the power of $4$ .

$\frac{- 150 + 138 - 1 \cdot 1296}{6}$

Step 3.6

Multiply $- 1$ by $1296$ .

$\frac{- 150 + 138 - 1296}{6}$

Step 4

Simplify the expression.

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Step 4.1

Add $- 150$ and $138$ .

$\frac{- 12 - 1296}{6}$

Step 4.2

Subtract $1296$ from $- 12$ .

$\frac{- 1308}{6}$

Step 4.3

Divide $- 1308$ by $6$ .

$- 218$