Question

Simplify $\frac{8^2 \times 3^3}{\sqrt{64} \times \sqrt{81}}$.

• A. 24
• B. 27
• C. 72
• D. 64

Answer 1

Answer:

A. 24

The simplified value of the given expression is 24.

$\frac{8^2 \times 3^3}{\sqrt{64} \times \sqrt{81}}$

1. Find the value of each individual term:

   • 8² = 8 × 8 = 64

   • 3³ = 3 × 3 × 3 = 27

   • $\sqrt{64} = 8$

   • $\sqrt{81} = 9$

2. Substitute these values back into the expression:
   $\frac{64 \times 27}{8 \times 9}$

3. Simplify the fraction by cancellation:

   • Divide 64 by 8: $\frac{64}{8} = 8$

   • Divide 27 by 9: $\frac{27}{9} = 3$

   Now multiply the remaining numbers:
   $8 \times 3 = \mathbf{24}$