Evaluate square root of ((910^9)|(35010^-9)(-150*10^-9)|)/50

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

Group coefficients together and exponents together to multiply numbers in scientific notation.

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

Multiply $350$ by $- 150$ .

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

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

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

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

Subtract $9$ from $- 9$ .

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

Simplify the numerator.

Write $- 52500 \cdot 10^{- 18}$ in proper scientific notation.

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

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

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

Combine exponents.

Multiply $5.25$ by $9$ .

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

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

Move $10^{- 14}$ .

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

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

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

Add $- 14$ and $9$ .

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

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

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

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

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

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

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

Simplify by dividing numbers.

Divide $47.25$ by $100000$ .

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

Divide $0.0004725$ by $50$ .

$\sqrt{0.00000945}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{0.00000945}$

Decimal Form:

$0.00307408 \dots$

Evaluate square root of ((9*10^9)|(350*10^-9)(-150*10^-9)|)/50