Algebra Examples

$\frac{\sqrt{2^{6}} + (11 - 5^{2})}{| - 10 - 2 \cdot 3 |}$

Step 1

Remove parentheses.

$\frac{\sqrt{2^{6}} + 11 - 5^{2}}{| - 10 - 2 \cdot 3 |}$

Step 2

Simplify the numerator.

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Step 2.1

Raise $2$ to the power of $6$ .

$\frac{\sqrt{64} + 11 - 5^{2}}{| - 10 - 2 \cdot 3 |}$

Step 2.2

Rewrite $64$ as $8^{2}$ .

$\frac{\sqrt{8^{2}} + 11 - 5^{2}}{| - 10 - 2 \cdot 3 |}$

Step 2.3

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

$\frac{8 + 11 - 5^{2}}{| - 10 - 2 \cdot 3 |}$

Step 2.4

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

$\frac{8 + 11 - 1 \cdot 25}{| - 10 - 2 \cdot 3 |}$

Step 2.5

Multiply $- 1$ by $25$ .

$\frac{8 + 11 - 25}{| - 10 - 2 \cdot 3 |}$

Step 2.6

Add $8$ and $11$ .

$\frac{19 - 25}{| - 10 - 2 \cdot 3 |}$

Step 2.7

Subtract $25$ from $19$ .

$\frac{- 6}{| - 10 - 2 \cdot 3 |}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $- 2$ by $3$ .

$\frac{- 6}{| - 10 - 6 |}$

Step 3.2

Subtract $6$ from $- 10$ .

$\frac{- 6}{| - 16 |}$

Step 3.3

The absolute value is the distance between a number and zero. The distance between $- 16$ and $0$ is $16$ .

$\frac{- 6}{16}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $- 6$ and $16$ .

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Step 4.1.1

Factor $2$ out of $- 6$ .

$\frac{2 (- 3)}{16}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $2$ out of $16$ .

$\frac{2 \cdot - 3}{2 \cdot 8}$

Step 4.1.2.2

Cancel the common factor.

$\frac{2 \cdot - 3}{2 \cdot 8}$

Step 4.1.2.3

Rewrite the expression.

$\frac{- 3}{8}$

Step 4.2

Move the negative in front of the fraction.

$- \frac{3}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{8}$

Decimal Form:

$- 0.375$