Solve (1/2)^-3(1/4)^-2/(frac{1{4})^3*(1/3)^-3}

$$\frac { ( \frac { 1 } { 2 } ) ^ { - 3 } ( \frac { 1 } { 4 } ) ^ { - 2 } } { ( \frac { 1 } { 4 } ) ^ { 3 } * ( \frac { 1 } { 3 } ) ^ { - 3 } }$$

Evaluate

$$\frac{8192}{27}\approx 303.407407407$$

Solution Steps

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

$$\frac{\left(\frac{1}{2}\right)^{-3}}{\left(\frac{1}{4}\right)^{5}\times \left(\frac{1}{3}\right)^{-3}}$$

Calculate \frac{1}{2} to the power of -3 and get 8.

$$\frac{8}{\left(\frac{1}{4}\right)^{5}\times \left(\frac{1}{3}\right)^{-3}}$$

Calculate \frac{1}{4} to the power of 5 and get \frac{1}{1024}.

$$\frac{8}{\frac{1}{1024}\times \left(\frac{1}{3}\right)^{-3}}$$

Calculate \frac{1}{3} to the power of -3 and get 27.

$$\frac{8}{\frac{1}{1024}\times 27}$$

Multiply \frac{1}{1024} and 27 to get \frac{27}{1024}.

$$\frac{8}{\frac{27}{1024}}$$

Divide 8 by \frac{27}{1024} by multiplying 8 by the reciprocal of \frac{27}{1024}.

$$8\times \frac{1024}{27}$$

Multiply 8 and \frac{1024}{27} to get \frac{8192}{27}.

$$\frac{8192}{27}$$

Factor

$$\frac{2 ^ {13}}{3 ^ {3}} = 303\frac{11}{27} = 303.4074074074074$$