Solve 5.3*10^-6(1.06*10^-5+10^-12)^2=

$$5.3 \times 10 ^ { - 6 } ( 1.06 \times 10 ^ { - 5 } + 10 ^ { - 12 } ) ^ { 2 } =$$

Evaluate

$$0.0000000000000005955081123600053$$

Solution Steps

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

$$5.3\times \frac{1}{1000000}\left(1.06\times 10^{-5}+10^{-12}\right)^{2}$$

Multiply 5.3 and \frac{1}{1000000} to get \frac{53}{10000000}.

$$\frac{53}{10000000}\left(1.06\times 10^{-5}+10^{-12}\right)^{2}$$

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

$$\frac{53}{10000000}\left(1.06\times \frac{1}{100000}+10^{-12}\right)^{2}$$

Multiply 1.06 and \frac{1}{100000} to get \frac{53}{5000000}.

$$\frac{53}{10000000}\left(\frac{53}{5000000}+10^{-12}\right)^{2}$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$\frac{53}{10000000}\left(\frac{53}{5000000}+\frac{1}{1000000000000}\right)^{2}$$

Add \frac{53}{5000000} and \frac{1}{1000000000000} to get \frac{10600001}{1000000000000}.

$$\frac{53}{10000000}\times \left(\frac{10600001}{1000000000000}\right)^{2}$$

Calculate \frac{10600001}{1000000000000} to the power of 2 and get \frac{112360021200001}{1000000000000000000000000}.

$$\frac{53}{10000000}\times \frac{112360021200001}{1000000000000000000000000}$$

Multiply \frac{53}{10000000} and \frac{112360021200001}{1000000000000000000000000} to get \frac{5955081123600053}{10000000000000000000000000000000}.

$$\frac{5955081123600053}{10000000000000000000000000000000}$$

Factor

$$\frac{53 \cdot 139 ^ {2} \cdot 76259 ^ {2}}{2 ^ {31} \cdot 5 ^ {31}} = 5.955081123600054 \times 10^{-16}$$