Basic Math Examples

50 \div (- 5) + (- 1 - {(- 2)}^{5} \div {(- 2)}^{3})

$50 \div (- 5) + (- 1 - {(- 2)}^{5} \div {(- 2)}^{3})$

Step 1

Remove parentheses.

50 \div (- 5) - 1 - {(- 2)}^{5} \div {(- 2)}^{3}

$50 \div (- 5) - 1 - {(- 2)}^{5} \div {(- 2)}^{3}$

Step 2

Simplify each term.

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Step 2.1

Divide

50

$50$ by

- 5

$- 5$ .

- 10 - 1 - {(- 2)}^{5} \div {(- 2)}^{3}

$- 10 - 1 - {(- 2)}^{5} \div {(- 2)}^{3}$

Step 2.2

Rewrite the division as a fraction.

- 10 - 1 - \frac{{(- 2)}^{5}}{{(- 2)}^{3}}

$- 10 - 1 - \frac{{(- 2)}^{5}}{{(- 2)}^{3}}$

Step 2.3

Cancel the common factor of

{(- 2)}^{5}

${(- 2)}^{5}$ and

{(- 2)}^{3}

${(- 2)}^{3}$ .

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Step 2.3.1

Factor

{(- 2)}^{3}

${(- 2)}^{3}$ out of

{(- 2)}^{5}

${(- 2)}^{5}$ .

- 10 - 1 - \frac{{(- 2)}^{3} {(- 2)}^{2}}{{(- 2)}^{3}}

$- 10 - 1 - \frac{{(- 2)}^{3} {(- 2)}^{2}}{{(- 2)}^{3}}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Multiply by

1

$1$ .

- 10 - 1 - \frac{{(- 2)}^{3} {(- 2)}^{2}}{{(- 2)}^{3} \cdot 1}

$- 10 - 1 - \frac{{(- 2)}^{3} {(- 2)}^{2}}{{(- 2)}^{3} \cdot 1}$

Step 2.3.2.2

Cancel the common factor.

$- 10 - 1 - \frac{{(- 2)}^{3} {(- 2)}^{2}}{{(- 2)}^{3} \cdot 1}$

Step 2.3.2.3

Rewrite the expression.

$- 10 - 1 - \frac{{(- 2)}^{2}}{1}$

Step 2.3.2.4

Divide

${(- 2)}^{2}$ by

$1$ .

$- 10 - 1 - {(- 2)}^{2}$

Step 2.4

Raise

$- 2$ to the power of

$2$ .

$- 10 - 1 - 1 \cdot 4$

Step 2.5

Multiply

$- 1$ by

$4$ .

$- 10 - 1 - 4$

Step 3

Simplify by subtracting numbers.

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Step 3.1

Subtract

$1$ from

$- 10$ .

$- 11 - 4$

Step 3.2

Subtract

$4$ from

$- 11$ .

$- 15$