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

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

Evaluate

$$4$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

Calculate 1 to the power of 2 and get 1.

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

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

$$\frac{1}{2\times \frac{1}{8}}$$

Multiply 2 and \frac{1}{8} to get \frac{1}{4}.

$$\frac{1}{\frac{1}{4}}$$

Divide 1 by \frac{1}{4} by multiplying 1 by the reciprocal of \frac{1}{4}.

$$1\times 4$$

Multiply 1 and 4 to get 4.

$$4$$

Factor

$$2^{2}$$