Q. \( \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \)

Compute the product \( \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \).

1. Recognize the repeated multiplication of the same factor. Six factors of \( \frac{1}{2} \) can be written with an exponent:

   \[ \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \left(\frac{1}{2}\right)^6 \]

   Reason: multiplying the same number by itself \( n \) times equals that number to the \( n \)-th power.

2. Use the power-of-a-fraction rule: for integers \( a \), \( b \) and positive integer \( n \), \( \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \). Apply it here:

   \[ \left(\frac{1}{2}\right)^6 = \frac{1^6}{2^6} \]

3. Compute numerator and denominator separately:

   • Numerator: \( 1^6 = 1 \) because any power of 1 is 1.

   • Denominator: compute powers of 2 step by step:
     \( 2^2 = 4 \),
     \( 2^3 = 8 \),
     \( 2^4 = 16 \),
     \( 2^5 = 32 \),
     \( 2^6 = 64 \).

4. Combine the results:

   \[ \left(\frac{1}{2}\right)^6 = \frac{1}{64} \]

5. Optional: express as a decimal if desired: \( \frac{1}{64} = 0.015625 \).

\( \frac{1}{64} \).