Question

\[\left\{ \frac{2^{\frac{2}{5}} \times 3^{\frac{1}{5}} \times 4^{\frac{4}{5}}}{10^{\frac{-1}{5}} \times 5^{\frac{3}{5}}} \div \frac{3^{\frac{3}{5}} \times 5^{-\frac{7}{5}}}{4^{\frac{-3}{5}} \times 6} \right\} \times 2 =\]

• A. 10
• B. 20
• C. 30
• D. 40

Answer 1

The Correct Option is B

Step 1: Convert all terms to bases 2, 3 and 5 — \( 4 = 2^2 \), \( 10 = 2 \times 5 \), \( 6 = 2 \times 3 \).

Step 2: Collecting powers of 2 across the full expression, including both fractions and the final \( \times 2 \), gives a total exponent of 3, so the 2-part is \( 2^3 = 8 \).

Step 3: Collecting powers of 5 gives a total exponent of 1, so the 5-part is \( 5^1 = 5 \); the powers of 3 cancel out completely across the numerator and denominator.

Step 4: Multiply the surviving parts together. \[ \boxed{8 \times 5 = 40} \]