Solve 120(1/2)^7(1/2)^3

$$120 ( \frac { 1 } { 2 } ) ^ { 7 } ( \frac { 1 } { 2 } ) ^ { 3 }$$

Evaluate

$$\frac{15}{128}=0.1171875$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$120\times \left(\frac{1}{2}\right)^{10}$$

Calculate \frac{1}{2} to the power of 10 and get \frac{1}{1024}.

$$120\times \frac{1}{1024}$$

Multiply 120 and \frac{1}{1024} to get \frac{120}{1024}.

$$\frac{120}{1024}$$

Reduce the fraction \frac{120}{1024} to lowest terms by extracting and canceling out 8.

$$\frac{15}{128}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {7}} = 0.1171875$$