Basic Math Examples

$- 24 - {| - 10 - (- {(- 3 + 4 - 2)}^{7}) |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Add $- 3$ and $4$ .

$- 24 - {| - 10 - - {(1 - 2)}^{7} |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.1.2

Subtract $2$ from $1$ .

$- 24 - {| - 10 - - {(- 1)}^{7} |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.1.3

Multiply $- 1$ by ${(- 1)}^{7}$ by adding the exponents.

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Step 1.1.3.1

Move ${(- 1)}^{7}$ .

$- 24 - {| - 10 + {(- 1)}^{7} \cdot - 1 \cdot - 1 |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.1.3.2

Multiply ${(- 1)}^{7}$ by $- 1$ .

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Step 1.1.3.2.1

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

$- 24 - {| - 10 + {(- 1)}^{7} \cdot {(- 1)}^{1} \cdot - 1 |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.1.3.2.2

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

$- 24 - {| - 10 + {(- 1)}^{7 + 1} \cdot - 1 |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.1.3.3

Add $7$ and $1$ .

$- 24 - {| - 10 + {(- 1)}^{8} \cdot - 1 |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.1.4

Multiply ${(- 1)}^{8}$ by $- 1$ by adding the exponents.

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Step 1.1.4.1

Multiply ${(- 1)}^{8}$ by $- 1$ .

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Step 1.1.4.1.1

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

$- 24 - {| - 10 + {(- 1)}^{8} \cdot {(- 1)}^{1} |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.1.4.1.2

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

$- 24 - {| - 10 + {(- 1)}^{8 + 1} |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.1.4.2

Add $8$ and $1$ .

$- 24 - {| - 10 + {(- 1)}^{9} |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.1.5

Raise $- 1$ to the power of $9$ .

$- 24 - {| - 10 - 1 |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.2

Subtract $1$ from $- 10$ .

$- 24 - {| - 11 |}^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $- 11$ and $0$ is $11$ .

$- 24 - 11^{2} - \sqrt[3]{40 \div (- 5)}$

Step 1.4

Raise $11$ to the power of $2$ .

$- 24 - 1 \cdot 121 - \sqrt[3]{40 \div (- 5)}$

Step 1.5

Multiply $- 1$ by $121$ .

$- 24 - 121 - \sqrt[3]{40 \div (- 5)}$

Step 1.6

Divide $40$ by $- 5$ .

$- 24 - 121 - \sqrt[3]{- 8}$

Step 1.7

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$- 24 - 121 - \sqrt[3]{{(- 2)}^{3}}$

Step 1.8

Pull terms out from under the radical, assuming real numbers.

$- 24 - 121 - - 2$

Step 1.9

Multiply $- 1$ by $- 2$ .

$- 24 - 121 + 2$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Subtract $121$ from $- 24$ .

$- 145 + 2$

Step 2.2

Add $- 145$ and $2$ .

$- 143$