Solve (1/2)^2*1/2*(1/2)^3=(1/8)^6=frac{1}{262,144}

$$( \frac { 1 } { 2 } ) ^ { 2 } \times \frac { 1 } { 2 } \times ( \frac { 1 } { 2 } ) ^ { 3 } = ( \frac { 1 } { 8 } ) ^ { 6 } = \frac { 1 } { 262,144 }$$

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\left(\frac{1}{2}\right)^{3}\times \left(\frac{1}{2}\right)^{3}=\left(\frac{1}{8}\right)^{6}\text{ and }\left(\frac{1}{8}\right)^{6}=\frac{1}{262144}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\left(\frac{1}{2}\right)^{6}=\left(\frac{1}{8}\right)^{6}\text{ and }\left(\frac{1}{8}\right)^{6}=\frac{1}{262144}$$

Calculate \frac{1}{2} to the power of 6 and get \frac{1}{64}.

$$\frac{1}{64}=\left(\frac{1}{8}\right)^{6}\text{ and }\left(\frac{1}{8}\right)^{6}=\frac{1}{262144}$$

Calculate \frac{1}{8} to the power of 6 and get \frac{1}{262144}.

$$\frac{1}{64}=\frac{1}{262144}\text{ and }\left(\frac{1}{8}\right)^{6}=\frac{1}{262144}$$

Least common multiple of 64 and 262144 is 262144. Convert \frac{1}{64} and \frac{1}{262144} to fractions with denominator 262144.

$$\frac{4096}{262144}=\frac{1}{262144}\text{ and }\left(\frac{1}{8}\right)^{6}=\frac{1}{262144}$$

Compare \frac{4096}{262144} and \frac{1}{262144}.

$$\text{false}\text{ and }\left(\frac{1}{8}\right)^{6}=\frac{1}{262144}$$

Calculate \frac{1}{8} to the power of 6 and get \frac{1}{262144}.

$$\text{false}\text{ and }\frac{1}{262144}=\frac{1}{262144}$$

Compare \frac{1}{262144} and \frac{1}{262144}.

$$\text{false}\text{ and }\text{true}$$

The conjunction of \text{false} and \text{true} is \text{false}.

$$\text{false}$$