Algebra Examples

${(8)}^{0.5}$

Step 1

Remove parentheses.

$8^{0.5}$

Step 2

Change $0.5$ into a fraction.

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Step 2.1

Multiply by $\frac{10}{10}$ to remove the decimal.

$8^{\frac{10 \cdot 0.5}{10}}$

Step 2.2

Multiply $10$ by $0.5$ .

$8^{\frac{5}{10}}$

Step 2.3

Cancel the common factor of $5$ and $10$ .

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Step 2.3.1

Factor $5$ out of $5$ .

$8^{\frac{5 (1)}{10}}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $5$ out of $10$ .

$8^{\frac{5 \cdot 1}{5 \cdot 2}}$

Step 2.3.2.2

Cancel the common factor.

$8^{\frac{5 \cdot 1}{5 \cdot 2}}$

Step 2.3.2.3

Rewrite the expression.

$8^{\frac{1}{2}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{8^{1}}$

Step 4

Anything raised to $1$ is the base itself.

$\sqrt{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{8}$

Decimal Form:

$2.82842712 \dots$