Solve sqrt{9*10^9*10^-6*10^-8/910^-3}

$$\sqrt{ \frac{ 9 \times { 10 }^{ 9 } \times { 10 }^{ -6 } \times { 10 }^{ -8 } }{ 9 { 10 }^{ -3 } } }$$

Evaluate

$$\frac{1}{10}=0.1$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and -6 to get 3.

$$\sqrt{\frac{9\times 10^{3}\times 10^{-8}}{9\times 10^{-3}}}$$

To multiply powers of the same base, add their exponents. Add 3 and -8 to get -5.

$$\sqrt{\frac{9\times 10^{-5}}{9\times 10^{-3}}}$$

Cancel out 9 in both numerator and denominator.

$$\sqrt{\frac{10^{-5}}{10^{-3}}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\sqrt{\frac{1}{10^{2}}}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt{\frac{1}{100}}$$

Rewrite the square root of the division \frac{1}{100} as the division of square roots \frac{\sqrt{1}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$\frac{1}{10}$$

Factor

$$\frac{1}{2 \cdot 5} = 0.1$$