Solve =4pi*10^-7*(500)^2*3.14*(10*10^-2)^2/0.25

$$= \frac { 4 \pi \times 10 ^ { - 7 } \times ( 500 ) ^ { 2 } \times 3.14 \times ( 10 \times 10 ^ { - 2 } ) ^ { 2 } } { 0.25 }$$

Evaluate

$$\frac{157\pi }{12500}\approx 0.039458404$$

Solution Steps

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

$$\frac{4\pi \times 10^{-7}\times 500^{2}\times 3.14\times \left(10^{-1}\right)^{2}}{0.25}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{4\pi \times 10^{-7}\times 500^{2}\times 3.14\times 10^{-2}}{0.25}$$

To multiply powers of the same base, add their exponents. Add -7 and -2 to get -9.

$$\frac{4\pi \times 10^{-9}\times 500^{2}\times 3.14}{0.25}$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\frac{4\pi \times \frac{1}{1000000000}\times 500^{2}\times 3.14}{0.25}$$

Multiply 4 and \frac{1}{1000000000} to get \frac{1}{250000000}.

$$\frac{\frac{1}{250000000}\pi \times 500^{2}\times 3.14}{0.25}$$

Calculate 500 to the power of 2 and get 250000.

$$\frac{\frac{1}{250000000}\pi \times 250000\times 3.14}{0.25}$$

Multiply \frac{1}{250000000} and 250000 to get \frac{1}{1000}.

$$\frac{\frac{1}{1000}\pi \times 3.14}{0.25}$$

Multiply \frac{1}{1000} and 3.14 to get \frac{157}{50000}.

$$\frac{\frac{157}{50000}\pi }{0.25}$$

Divide \frac{157}{50000}\pi by 0.25 to get \frac{157}{12500}\pi .

$$\frac{157}{12500}\pi$$

Expand

$$\frac{157 \pi}{12500} = 0.0394584037290878$$

Solution Steps

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

$$\frac{4\pi \times 10^{-7}\times 500^{2}\times 3.14\times \left(10^{-1}\right)^{2}}{0.25}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{4\pi \times 10^{-7}\times 500^{2}\times 3.14\times 10^{-2}}{0.25}$$

To multiply powers of the same base, add their exponents. Add -7 and -2 to get -9.

$$\frac{4\pi \times 10^{-9}\times 500^{2}\times 3.14}{0.25}$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\frac{4\pi \times \frac{1}{1000000000}\times 500^{2}\times 3.14}{0.25}$$

Multiply 4 and \frac{1}{1000000000} to get \frac{1}{250000000}.

$$\frac{\frac{1}{250000000}\pi \times 500^{2}\times 3.14}{0.25}$$

Calculate 500 to the power of 2 and get 250000.

$$\frac{\frac{1}{250000000}\pi \times 250000\times 3.14}{0.25}$$

Multiply \frac{1}{250000000} and 250000 to get \frac{1}{1000}.

$$\frac{\frac{1}{1000}\pi \times 3.14}{0.25}$$

Multiply \frac{1}{1000} and 3.14 to get \frac{157}{50000}.

$$\frac{\frac{157}{50000}\pi }{0.25}$$

Divide \frac{157}{50000}\pi by 0.25 to get \frac{157}{12500}\pi .

$$\frac{157}{12500}\pi$$