Exponent rules unit test

Question

Use the product rule of exponents to simplify 5 10.5 5

Answer 1

To simplify the expression 5^10.5^5 using the product rule of exponents, we need to multiply the powers:

5^10.5^5 = (5^10.5) × (5^5)

Now, let's simplify each part separately:

5^10.5 = (5^10)^0.5 = 9765625^0.5 (using the power rule of exponents)

Similarly,

5^5 = 3125

So, the expression becomes:

(9765625^0.5) × 3125

Now, we can calculate 9765625^0.5 by finding the square root of 9765625:

9765625^0.5 = √9765625 = 3125

Therefore, the expression simplifies to:

3125 × 3125 = 9765625