Question

evaluate the following expression, if possible.

\\625^{\frac{3}{4}}\\

select the correct choice below and fill in any answer boxes in your choice.

a. \\625^{\frac{3}{4}} = \\

b. the solution is not a real number.

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Rewrite using radicals

$$ 625^{\frac{3}{4}} = (\sqrt[4]{625})^3 $$

Step 2: Evaluate the fourth root

$$ \sqrt[4]{625} = 5 \quad \text{since} \quad 5^4 = 625 $$

Step 3: Cube the result

$$ 5^3 = 125 $$

Answer:

A. \(625^{\frac{3}{4}} = 125\)