Solve ((1/2)^{2})^3*2^5/2^3*(1/2)^-2

$$( ( \frac { 1 } { 2 } ) ^ { 2 } ) ^ { 3 } \cdot \frac { 2 ^ { 5 } } { 2 ^ { 3 } } \cdot ( \frac { 1 } { 2 } ) ^ { - 2 }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\frac{1}{2}\right)^{6}\times \frac{2^{5}}{2^{3}}\times \left(\frac{1}{2}\right)^{-2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

$$\left(\frac{1}{2}\right)^{6}\times 2^{2}\times \left(\frac{1}{2}\right)^{-2}$$

To multiply powers of the same base, add their exponents. Add 6 and -2 to get 4.

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

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$\frac{1}{16}\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{16}\times 4$$

Multiply \frac{1}{16} and 4 to get \frac{1}{4}.

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

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$