Solve (2^-1x^-1)div2^-2=(1/2)^1

$$( 2 ^ { - 1 } x ^ { - 1 } ) \div 2 ^ { - 2 } = ( \frac { 1 } { 2 } ) ^ { 1 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

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

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

Express 2^{1}\times \frac{1}{x} as a single fraction.

$$\frac{2^{1}}{x}=\left(\frac{1}{2}\right)^{1}$$

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

$$\frac{2^{1}}{x}=\frac{1}{2}$$

Calculate 2 to the power of 1 and get 2.

$$\frac{2}{x}=\frac{1}{2}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of x,2.

$$2\times 2=x$$

Multiply 2 and 2 to get 4.

$$4=x$$

Swap sides so that all variable terms are on the left hand side.

$$x=4$$