Algebra Examples

$\sqrt{\frac{(9 \cdot 10^{9}) | (350 \cdot 10^{- 9}) (- 150 \cdot 10^{- 9}) |}{50}}$

Step 1

Multiply $350$ by $- 150$ .

$\sqrt{\frac{9 \cdot 10^{9} | - 52500 (10^{- 9} \cdot 10^{- 9}) |}{50}}$

Step 2

Multiply $10^{- 9}$ by $10^{- 9}$ by adding the exponents.

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Step 2.1

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

$\sqrt{\frac{9 \cdot 10^{9} | - 52500 \cdot 10^{- 9 - 9} |}{50}}$

Step 2.2

Subtract $9$ from $- 9$ .

$\sqrt{\frac{9 \cdot 10^{9} | - 52500 \cdot 10^{- 18} |}{50}}$

Step 3

Simplify the numerator.

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Step 3.1

Move the decimal point in $- 52500$ to the left by $4$ places and increase the power of $10^{- 18}$ by $4$ .

$\sqrt{\frac{9 \cdot 10^{9} | - 5.25 \cdot 10^{- 14} |}{50}}$

Step 3.2

$- 5.25 \cdot 10^{- 14}$ is approximately $0$ which is negative so negate $- 5.25 \cdot 10^{- 14}$ and remove the absolute value

$\sqrt{\frac{9 \cdot 10^{9} \cdot 5.25 \cdot 10^{- 14}}{50}}$

Step 3.3

Combine exponents.

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Step 3.3.1

Multiply $5.25$ by $9$ .

$\sqrt{\frac{47.25 \cdot 10^{9} \cdot 10^{- 14}}{50}}$

Step 3.3.2

Multiply $10^{9}$ by $10^{- 14}$ by adding the exponents.

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Step 3.3.2.1

Move $10^{- 14}$ .

$\sqrt{\frac{47.25 \cdot (10^{- 14} \cdot 10^{9})}{50}}$

Step 3.3.2.2

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

$\sqrt{\frac{47.25 \cdot 10^{- 14 + 9}}{50}}$

Step 3.3.2.3

Add $- 14$ and $9$ .

$\sqrt{\frac{47.25 \cdot 10^{- 5}}{50}}$

Step 3.4

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

$\sqrt{\frac{47.25 \cdot \frac{1}{10^{5}}}{50}}$

Step 3.5

Raise $10$ to the power of $5$ .

$\sqrt{\frac{47.25 \cdot \frac{1}{100000}}{50}}$

Step 4

Combine $47.25$ and $\frac{1}{100000}$ .

$\sqrt{\frac{\frac{47.25}{100000}}{50}}$

Step 5

Simplify by dividing numbers.

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Step 5.1

Divide $47.25$ by $100000$ .

$\sqrt{\frac{0.0004725}{50}}$

Step 5.2

Divide $0.0004725$ by $50$ .

$\sqrt{0.00000945}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{0.00000945}$

Decimal Form:

$0.00307408 \dots$