Q. What is \( \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \)?

Q: What is the product of \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 = \frac{1}{64}.

Q: How do you compute this quickly?

Use exponents: multiply six identical factors gives (1/2)^6 . Or halve 1 six times.

Q: How do you multiply fractions in general?

Multiply numerators and denominators: \frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd} .

Q: How is this written using powers of 2?

\left(\frac{1}{2}\right)^6 = 2^{-6} = \frac{1}{2^6}.

Q: What is the reciprocal?

The reciprocal is 64 because \frac{1}{1/64}=64.

Answer

Compute the product as a power:
\[
\left(\tfrac{1}{2}\right)^6=\frac{1^6}{2^6}=\frac{1}{64}.
\]

Final result: \(\boxed{\tfrac{1}{64}}\).

Detailed Explanation

Write the product as a power because the same factor appears six times:
\( \left(\tfrac{1}{2}\right)^6 \)
Raise numerator and denominator separately (power of a fraction):
\( \left(\tfrac{1}{2}\right)^6 = \dfrac{1^6}{2^6} \)
Compute the powers:
\( \dfrac{1^6}{2^6} = \dfrac{1}{64} \)
Final answer:
\( \boxed{\dfrac{1}{64}} \)

Try our AI homework help tools: get answers fast!

Use AI

FAQs

What is the product of \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\)?

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

How do you compute this quickly?

Use exponents: multiply six identical factors gives \( (1/2)^6 \). Or halve 1 six times.

Why is it \( (1/2)^6 \) and not something else?

Repeated multiplication of the same number n times equals that number to the nth power: \(a\cdot a\cdot\ldots\cdot a = a^n\).

How do you multiply fractions in general?

Multiply numerators and denominators: \( \frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd} \).

What is the decimal form?

\(\frac{1}{64} = 0.015625\).

What is the percent?

How is this written using powers of 2?

\(\left(\frac{1}{2}\right)^6 = 2^{-6} = \frac{1}{2^6}\).

What is the reciprocal?

The reciprocal is \(64\) because \( \frac{1}{1/64}=64.\)

Math AI tools solve different problems.
Find your favorite today!

173,935+ happy customers
Math, Calculus, Geometry, etc.

✅ AI math helper 👤 AI geometry solver ✏️ AI calculus help