Q. One half to the power of 6 is \( \left(\tfrac{1}{2}\right)^6 = \tfrac{1}{64} \).

Problem

Compute one half to the power of 6.

1. Write the expression in mathematical form:
   \[ \left(\frac{1}{2}\right)^6 \]
2. Use the exponent rule for a quotient: for any nonzero \( a \) and \( b \) and integer \( n \),
   \[ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \]
   Apply this with \( a = 1 \), \( b = 2 \), \( n = 6 \):
   \[ \left(\frac{1}{2}\right)^6 = \frac{1^6}{2^6} \]
3. Compute the numerator and denominator separately.

   Numerator:
   \[ 1^6 = 1 \]
   Denominator (compute 2 multiplied by itself 6 times):
   \[ 2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64 \]

4. Combine the results:
   \[ \left(\frac{1}{2}\right)^6 = \frac{1}{64} \]

\[ \frac{1}{64} \]