Solve 49*2^-3/7^-3*10*2^-5

$$\frac { 49 \times 2 ^ { - 3 } } { 7 ^ { - 3 } \times 10 \times 2 ^ { - 5 } }$$

Evaluate

$$\frac{33614}{5}=6722.8$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{49\times 2^{2}}{10\times 7^{-3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{49\times 4}{10\times 7^{-3}}$$

Multiply 49 and 4 to get 196.

$$\frac{196}{10\times 7^{-3}}$$

Calculate 7 to the power of -3 and get \frac{1}{343}.

$$\frac{196}{10\times \frac{1}{343}}$$

Multiply 10 and \frac{1}{343} to get \frac{10}{343}.

$$\frac{196}{\frac{10}{343}}$$

Divide 196 by \frac{10}{343} by multiplying 196 by the reciprocal of \frac{10}{343}.

$$196\times \frac{343}{10}$$

Multiply 196 and \frac{343}{10} to get \frac{33614}{5}.

$$\frac{33614}{5}$$

Factor

$$\frac{2 \cdot 7 ^ {5}}{5} = 6722\frac{4}{5} = 6722.8$$