Solve sqrt{1/64*pi*(10*10^-3)^4/(25*10^-3)^2*pi}

$$\sqrt { \frac { \frac { 1 } { 64 } \times \pi \times ( 10 \times 10 ^ { - 3 } ) ^ { 4 } } { ( 25 \times 10 ^ { - 3 } ) ^ { 2 } \cdot \pi } }$$

Evaluate

$$\frac{1}{2000}=0.0005$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -3 to get -2.

$$\sqrt{\frac{\frac{1}{64}\pi \times \left(10^{-2}\right)^{4}}{\left(25\times 10^{-3}\right)^{2}\pi }}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 4 to get -8.

$$\sqrt{\frac{\frac{1}{64}\pi \times 10^{-8}}{\left(25\times 10^{-3}\right)^{2}\pi }}$$

Cancel out \pi in both numerator and denominator.

$$\sqrt{\frac{\frac{1}{64}\times 10^{-8}}{\left(25\times 10^{-3}\right)^{2}}}$$

Calculate 10 to the power of -8 and get \frac{1}{100000000}.

$$\sqrt{\frac{\frac{1}{64}\times \frac{1}{100000000}}{\left(25\times 10^{-3}\right)^{2}}}$$

Multiply \frac{1}{64} and \frac{1}{100000000} to get \frac{1}{6400000000}.

$$\sqrt{\frac{\frac{1}{6400000000}}{\left(25\times 10^{-3}\right)^{2}}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\sqrt{\frac{\frac{1}{6400000000}}{\left(25\times \frac{1}{1000}\right)^{2}}}$$

Multiply 25 and \frac{1}{1000} to get \frac{1}{40}.

$$\sqrt{\frac{\frac{1}{6400000000}}{\left(\frac{1}{40}\right)^{2}}}$$

Calculate \frac{1}{40} to the power of 2 and get \frac{1}{1600}.

$$\sqrt{\frac{\frac{1}{6400000000}}{\frac{1}{1600}}}$$

Divide \frac{1}{6400000000} by \frac{1}{1600} by multiplying \frac{1}{6400000000} by the reciprocal of \frac{1}{1600}.

$$\sqrt{\frac{1}{6400000000}\times 1600}$$

Multiply \frac{1}{6400000000} and 1600 to get \frac{1}{4000000}.

$$\sqrt{\frac{1}{4000000}}$$

Rewrite the square root of the division \frac{1}{4000000} as the division of square roots \frac{\sqrt{1}}{\sqrt{4000000}}. Take the square root of both numerator and denominator.

$$\frac{1}{2000}$$

Factor

$$\frac{1}{2 ^ {4} \cdot 5 ^ {3}} = 0.0005$$