Question

The value of \( 5^{2 \times \frac{1}{4}} - \left( \frac{5}{32} \times \frac{3}{5} \times \frac{7}{8} \times \frac{3}{16} \right) \) is:

• A. \( \frac{33}{16} \)
• B. \( \frac{67}{32} \)
• C. \( \frac{69}{32} \)
• D. \( \frac{17}{8} \)

Hint:

When solving complex expressions, break them down into simpler parts and simplify each step.

Answer 1

The Correct Option is B

To solve the expression, we first evaluate \( 5^{2 \times \frac{1}{4}} \) and then calculate the product of the other fractions.
First, compute \( 5^{2 \times \frac{1}{4}} \): \[ 5^{2 \times \frac{1}{4}} = 5^{\frac{1}{2}} = \sqrt{5} \] Next, compute the product of the fractions: \[ \frac{5}{32} \times \frac{3}{5} \times \frac{7}{8} \times \frac{3}{16} = \frac{5 \times 3 \times 7 \times 3}{32 \times 5 \times 8 \times 16} = \frac{315}{20480} = \frac{67}{32} \] Thus, the value of the expression is \( \frac{67}{32} \).