Solve [(1/3+1/6)^8*(1/2)^7]:[(1/2)^7]^2

$$[ ( \frac { 1 } { 3 } + \frac { 1 } { 6 } ) ^ { 8 } \cdot ( \frac { 1 } { 2 } ) ^ { 7 } ] : [ ( \frac { 1 } { 2 } ) ^ { 7 } ] ^ { 2 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{\left(\frac{1}{3}+\frac{1}{6}\right)^{8}\times \left(\frac{1}{2}\right)^{7}}{\left(\frac{1}{2}\right)^{14}}$$

Cancel out \left(\frac{1}{2}\right)^{7} in both numerator and denominator.

$$\frac{\left(\frac{1}{6}+\frac{1}{3}\right)^{8}}{\left(\frac{1}{2}\right)^{7}}$$

Add \frac{1}{6} and \frac{1}{3} to get \frac{1}{2}.

$$\frac{\left(\frac{1}{2}\right)^{8}}{\left(\frac{1}{2}\right)^{7}}$$

Calculate \frac{1}{2} to the power of 8 and get \frac{1}{256}.

$$\frac{\frac{1}{256}}{\left(\frac{1}{2}\right)^{7}}$$

Calculate \frac{1}{2} to the power of 7 and get \frac{1}{128}.

$$\frac{\frac{1}{256}}{\frac{1}{128}}$$

Divide \frac{1}{256} by \frac{1}{128} by multiplying \frac{1}{256} by the reciprocal of \frac{1}{128}.

$$\frac{1}{256}\times 128$$

Multiply \frac{1}{256} and 128 to get \frac{1}{2}.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$