Basic Math Examples

$\sqrt{10^{2 - 8^{2}}}$

Step 1

Simplify each term.

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Step 1.1

Raise $8$ to the power of $2$ .

$\sqrt{10^{2 - 1 \cdot 64}}$

Step 1.2

Multiply $- 1$ by $64$ .

$\sqrt{10^{2 - 64}}$

Step 2

Subtract $64$ from $2$ .

$\sqrt{10^{- 62}}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\sqrt{\frac{1}{10^{62}}}$

Step 4

Rewrite $\sqrt{\frac{1}{10^{62}}}$ as $\frac{\sqrt{1}}{\sqrt{10^{62}}}$ .

$\frac{\sqrt{1}}{\sqrt{10^{62}}}$

Step 5

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{10^{62}}}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite $10^{62}$ as ${(10^{31})}^{2}$ .

$\frac{1}{\sqrt{{(10^{31})}^{2}}}$

Step 6.2

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

$\frac{1}{10^{31}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{10^{31}}$

Decimal Form:

$1 \cdot 10^{- 31}$