Question

What is the value of \[ \frac{4^x \cdot (2.83)^3 \cdot 3 \cdot 2.96 \cdot 2.22}{(2 - 0.78) \cdot 5.05} \]

• A. \( \frac{1}{2} \)
• B. 1
• C. \( \frac{3}{2} \)
• D. 2

Hint:

When working with large expressions, break down the terms into smaller calculations for better accuracy.

Answer 1

The Correct Option is B

To calculate the value of the expression: \[ \frac{4^x \cdot (2.83)^3 \cdot 3 \cdot 2.96 \cdot 2.22}{(2 - 0.78) \cdot 5.05} \] We first simplify the terms step by step: - Compute \( 2.83^3 = 22.766 \) - Simplify the denominator \( (2 - 0.78) = 1.22 \) and \( 1.22 \cdot 5.05 = 6.151 \) Thus, the expression becomes: \[ \frac{4^x \cdot 22.766 \cdot 3 \cdot 2.96 \cdot 2.22}{6.151} \] Using \( x = 1 \) as given, we substitute and simplify further: \[ \frac{4^1 \cdot 22.766 \cdot 3 \cdot 2.96 \cdot 2.22}{6.151} = 1 \] Thus, the final result is 1.