Basic Math Examples

$\frac{{(- 8)}^{2}}{5 - 9} - {(- 1)}^{2} + 4 (- 9)$

Step 1

Find the common denominator.

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Step 1.1

Subtract $9$ from $5$ .

$\frac{{(- 8)}^{2}}{- 4} - {(- 1)}^{2} + 4 (- 9)$

Step 1.2

Multiply $\frac{{(- 8)}^{2}}{- 4}$ by $\frac{- 1}{- 1}$ .

$\frac{{(- 8)}^{2}}{- 4} \cdot \frac{- 1}{- 1} - {(- 1)}^{2} + 4 (- 9)$

Step 1.3

Multiply $\frac{{(- 8)}^{2}}{- 4}$ by $\frac{- 1}{- 1}$ .

$\frac{{(- 8)}^{2} \cdot - 1}{- 4 \cdot - 1} - {(- 1)}^{2} + 4 (- 9)$

Step 1.4

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

$\frac{{(- 8)}^{2} \cdot - 1}{- 4 \cdot - 1} + \frac{- {(- 1)}^{2}}{1} + 4 (- 9)$

Step 1.5

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

$\frac{{(- 8)}^{2} \cdot - 1}{- 4 \cdot - 1} + \frac{- {(- 1)}^{2}}{1} \cdot \frac{4}{4} + 4 (- 9)$

Step 1.6

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

$\frac{{(- 8)}^{2} \cdot - 1}{- 4 \cdot - 1} + \frac{- {(- 1)}^{2} \cdot 4}{4} + 4 (- 9)$

Step 1.7

Write $4 (- 9)$ as a fraction with denominator $1$ .

$\frac{{(- 8)}^{2} \cdot - 1}{- 4 \cdot - 1} + \frac{- {(- 1)}^{2} \cdot 4}{4} + \frac{4 (- 9)}{1}$

Step 1.8

Multiply $\frac{4 (- 9)}{1}$ by $\frac{4}{4}$ .

$\frac{{(- 8)}^{2} \cdot - 1}{- 4 \cdot - 1} + \frac{- {(- 1)}^{2} \cdot 4}{4} + \frac{4 (- 9)}{1} \cdot \frac{4}{4}$

Step 1.9

Multiply $\frac{4 (- 9)}{1}$ by $\frac{4}{4}$ .

$\frac{{(- 8)}^{2} \cdot - 1}{- 4 \cdot - 1} + \frac{- {(- 1)}^{2} \cdot 4}{4} + \frac{4 (- 9) \cdot 4}{4}$

Step 1.10

Multiply $- 4$ by $- 1$ .

$\frac{{(- 8)}^{2} \cdot - 1}{4} + \frac{- {(- 1)}^{2} \cdot 4}{4} + \frac{4 (- 9) \cdot 4}{4}$

Step 2

Combine the numerators over the common denominator.

$\frac{{(- 8)}^{2} \cdot - 1 - {(- 1)}^{2} \cdot 4 + 4 (- 9) \cdot 4}{4}$

Step 3

Simplify each term.

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Step 3.1

Raise $- 8$ to the power of $2$ .

$\frac{64 \cdot - 1 - {(- 1)}^{2} \cdot 4 + 4 (- 9) \cdot 4}{4}$

Step 3.2

Multiply $64$ by $- 1$ .

$\frac{- 64 - {(- 1)}^{2} \cdot 4 + 4 (- 9) \cdot 4}{4}$

Step 3.3

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 3.3.1

Multiply $- 1$ by ${(- 1)}^{2}$ .

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Step 3.3.1.1

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

$\frac{- 64 + {(- 1)}^{1} {(- 1)}^{2} \cdot 4 + 4 (- 9) \cdot 4}{4}$

Step 3.3.1.2

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

$\frac{- 64 + {(- 1)}^{1 + 2} \cdot 4 + 4 (- 9) \cdot 4}{4}$

Step 3.3.2

Add $1$ and $2$ .

$\frac{- 64 + {(- 1)}^{3} \cdot 4 + 4 (- 9) \cdot 4}{4}$

Step 3.4

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

$\frac{- 64 - 1 \cdot 4 + 4 (- 9) \cdot 4}{4}$

Step 3.5

Multiply $- 1$ by $4$ .

$\frac{- 64 - 4 + 4 (- 9) \cdot 4}{4}$

Step 3.6

Multiply $4 (- 9) \cdot 4$ .

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Step 3.6.1

Multiply $4$ by $- 9$ .

$\frac{- 64 - 4 - 36 \cdot 4}{4}$

Step 3.6.2

Multiply $- 36$ by $4$ .

$\frac{- 64 - 4 - 144}{4}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $4$ from $- 64$ .

$\frac{- 68 - 144}{4}$

Step 4.2

Subtract $144$ from $- 68$ .

$\frac{- 212}{4}$

Step 4.3

Divide $- 212$ by $4$ .

$- 53$