Accepted answer
Answer included
3 4 x 3 4 x 1 4
In Algebra and fraction practice, “3 4 x 3 4 x 1 4” is interpreted as the product of proper fractions \( \tfrac34 \times \tfrac34 \times \tfrac14 \).
Exact value in lowest terms
\[ \frac34 \times \frac34 \times \frac14 = \frac{3 \cdot 3 \cdot 1}{4 \cdot 4 \cdot 4} = \frac{9}{64}. \]
Lowest-terms verification: \(9=3^2\) and \(64=2^6\) share no common factor, so \(\gcd(9,64)=1\).
Equivalent forms
| Form | Expression | Value |
|---|---|---|
| Product form | \( \tfrac34 \times \tfrac34 \times \tfrac14 \) | \( \tfrac{9}{64} \) |
| Exponent form | \( \left(\tfrac34\right)^2 \times \tfrac14 \) | \( \tfrac{9}{64} \) |
| Prime-power form | \( \tfrac{3^2}{2^6} \) | \( \tfrac{9}{64} \) |
| Decimal form | \( \tfrac{9}{64} \) | \(0.140625\) |
Common pitfalls
- Denominator tracking errors: \(4 \cdot 4 \cdot 4 = 64\), not \(16\).
- Misreading shorthand: “3 4” is treated as \(\tfrac34\) (a fraction) rather than “34”.
- Reduction mistakes: \( \tfrac{9}{64} \) is already in lowest terms because 64 has only the prime factor 2.
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