Basic Math Examples

$- 1^{5} - {(- 1)}^{4} + {(- 1)}^{5} {(- 1)}^{2} - 1$

Step 1

Simplify each term.

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Step 1.1

One to any power is one.

$- 1 \cdot 1 - {(- 1)}^{4} + {(- 1)}^{5} {(- 1)}^{2} - 1$

Step 1.2

Multiply $- 1$ by $1$ .

$- 1 - {(- 1)}^{4} + {(- 1)}^{5} {(- 1)}^{2} - 1$

Step 1.3

Multiply $- 1$ by ${(- 1)}^{4}$ by adding the exponents.

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Step 1.3.1

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

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Step 1.3.1.1

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

$- 1 + {(- 1)}^{1} {(- 1)}^{4} + {(- 1)}^{5} {(- 1)}^{2} - 1$

Step 1.3.1.2

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

$- 1 + {(- 1)}^{1 + 4} + {(- 1)}^{5} {(- 1)}^{2} - 1$

Step 1.3.2

Add $1$ and $4$ .

$- 1 + {(- 1)}^{5} + {(- 1)}^{5} {(- 1)}^{2} - 1$

Step 1.4

Raise $- 1$ to the power of $5$ .

$- 1 - 1 + {(- 1)}^{5} {(- 1)}^{2} - 1$

Step 1.5

Multiply ${(- 1)}^{5}$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 1.5.1

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

$- 1 - 1 + {(- 1)}^{5 + 2} - 1$

Step 1.5.2

Add $5$ and $2$ .

$- 1 - 1 + {(- 1)}^{7} - 1$

Step 1.6

Raise $- 1$ to the power of $7$ .

$- 1 - 1 - 1 - 1$

Step 2

Simplify by subtracting numbers.

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Step 2.1

Subtract $1$ from $- 1$ .

$- 2 - 1 - 1$

Step 2.2

Subtract $1$ from $- 2$ .

$- 3 - 1$

Step 2.3

Subtract $1$ from $- 3$ .

$- 4$