Solve (200/6.3*10^-4*1.5*10^-2)^2*2*10^-5

$$( \frac { 200 } { 6.3 \times 10 ^ { - 4 } \times 1.5 \times 10 ^ { - 2 } } ) ^ { 2 } \times 2 \times 10 ^ { - 5 }$$

Evaluate

$$\frac{320000000000000}{35721}\approx 8958315836.62271493$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and -2 to get -6.

$$\left(\frac{200}{6.3\times 10^{-6}\times 1.5}\right)^{2}\times 2\times 10^{-5}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\left(\frac{200}{6.3\times \frac{1}{1000000}\times 1.5}\right)^{2}\times 2\times 10^{-5}$$

Multiply 6.3 and \frac{1}{1000000} to get \frac{63}{10000000}.

$$\left(\frac{200}{\frac{63}{10000000}\times 1.5}\right)^{2}\times 2\times 10^{-5}$$

Multiply \frac{63}{10000000} and 1.5 to get \frac{189}{20000000}.

$$\left(\frac{200}{\frac{189}{20000000}}\right)^{2}\times 2\times 10^{-5}$$

Divide 200 by \frac{189}{20000000} by multiplying 200 by the reciprocal of \frac{189}{20000000}.

$$\left(200\times \frac{20000000}{189}\right)^{2}\times 2\times 10^{-5}$$

Multiply 200 and \frac{20000000}{189} to get \frac{4000000000}{189}.

$$\left(\frac{4000000000}{189}\right)^{2}\times 2\times 10^{-5}$$

Calculate \frac{4000000000}{189} to the power of 2 and get \frac{16000000000000000000}{35721}.

$$\frac{16000000000000000000}{35721}\times 2\times 10^{-5}$$

Multiply \frac{16000000000000000000}{35721} and 2 to get \frac{32000000000000000000}{35721}.

$$\frac{32000000000000000000}{35721}\times 10^{-5}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\frac{32000000000000000000}{35721}\times \frac{1}{100000}$$

Multiply \frac{32000000000000000000}{35721} and \frac{1}{100000} to get \frac{320000000000000}{35721}.

$$\frac{320000000000000}{35721}$$

Factor

$$\frac{2 ^ {18} \cdot 5 ^ {13}}{3 ^ {6} \cdot 7 ^ {2}} = 8958315836\frac{22244}{35721} = 8958315836.622715$$