Question

If \( 5\sqrt{5} \times 5^3 \div 5^{-3/2} = 5^a \), then the value of \( a \) is:

• A. 8
• B. 5
• C. 6
• D. 4

Hint:

When working with powers of the same base, remember to add exponents when multiplying and subtract exponents when dividing.

Answer 1

The Correct Option is D

We start by simplifying the expression \( 5\sqrt{5} \times 5^3 \div 5^{-3/2} \): \[ 5\sqrt{5} = 5^{1 + 1/2} = 5^{3/2} \] Now the expression becomes: \[ 5^{3/2} \times 5^3 \div 5^{-3/2} \] Using the laws of exponents \( a^m \times a^n = a^{m+n} \) and \( \frac{a^m}{a^n} = a^{m-n} \), we combine the exponents: \[ 5^{3/2 + 3 - (-3/2)} = 5^{3/2 + 3 + 3/2} = 5^{6} \] Thus, \( a = 6 \), so the correct answer is (D) 4.