Linear Algebra Examples

$6.28 \sqrt{100^{- 12} \cdot 1^{- 3}}$

Step 1

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

$6.28 \sqrt{\frac{1}{100^{12}} \cdot 1^{- 3}}$

Step 2

Raise $100$ to the power of $12$ .

$6.28 \sqrt{\frac{1}{1000000000000000000000000} \cdot 1^{- 3}}$

Step 3

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

$6.28 \sqrt{\frac{1}{1000000000000000000000000} \cdot \frac{1}{1^{3}}}$

Step 4

One to any power is one.

$6.28 \sqrt{\frac{1}{1000000000000000000000000} \cdot \frac{1}{1}}$

Step 5

Divide $1$ by $1$ .

$6.28 \sqrt{\frac{1}{1000000000000000000000000} \cdot 1}$

Step 6

Multiply $\frac{1}{1000000000000000000000000}$ by $1$ .

$6.28 \sqrt{\frac{1}{1000000000000000000000000}}$

Step 7

Rewrite $\sqrt{\frac{1}{1000000000000000000000000}}$ as $\frac{\sqrt{1}}{\sqrt{1000000000000000000000000}}$ .

$6.28 \frac{\sqrt{1}}{\sqrt{1000000000000000000000000}}$

Step 8

Any root of $1$ is $1$ .

$6.28 \frac{1}{\sqrt{1000000000000000000000000}}$

Step 9

Simplify the denominator.

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Step 9.1

Rewrite $1000000000000000000000000$ as $1000000000000^{2}$ .

$6.28 \frac{1}{\sqrt{1000000000000^{2}}}$

Step 9.2

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

$6.28 (\frac{1}{1000000000000})$

Step 10

Combine fractions.

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Step 10.1

Combine $6.28$ and $\frac{1}{1000000000000}$ .

$\frac{6.28}{1000000000000}$

Step 10.2

Divide $6.28$ by $1000000000000$ .

$0$