Solve 5.12*10^-1div(2*10^-2)^3

$$5.12 \times 10 ^ { - 1 } \div ( 2 \times 10 ^ { - 2 } ) ^ { 3 }$$

Evaluate

$$64000$$

Solution Steps

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

$$\frac{5.12\times \frac{1}{10}}{\left(2\times 10^{-2}\right)^{3}}$$

Multiply 5.12 and \frac{1}{10} to get \frac{64}{125}.

$$\frac{\frac{64}{125}}{\left(2\times 10^{-2}\right)^{3}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\frac{64}{125}}{\left(2\times \frac{1}{100}\right)^{3}}$$

Multiply 2 and \frac{1}{100} to get \frac{1}{50}.

$$\frac{\frac{64}{125}}{\left(\frac{1}{50}\right)^{3}}$$

Calculate \frac{1}{50} to the power of 3 and get \frac{1}{125000}.

$$\frac{\frac{64}{125}}{\frac{1}{125000}}$$

Divide \frac{64}{125} by \frac{1}{125000} by multiplying \frac{64}{125} by the reciprocal of \frac{1}{125000}.

$$\frac{64}{125}\times 125000$$

Multiply \frac{64}{125} and 125000 to get 64000.

$$64000$$

Factor

$$2^{9}\times 5^{3}$$