Question

simplify the expression.

\\8^{\frac{1}{2}} \cdot 8^{\frac{3}{2}}\\

\\8^{\frac{1}{2}} \cdot 8^{\frac{3}{2}} = \square\\

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Apply the product rule of exponents

When multiplying terms with the same base, add their exponents:

$$ 8^{\frac{1}{2}} \cdot 8^{\frac{3}{2}} = 8^{\frac{1}{2} + \frac{3}{2}} $$

Step 2: Add the exponents

$$ \frac{1}{2} + \frac{3}{2} = \frac{4}{2} = 2 $$

Step 3: Evaluate the simplified expression

$$ 8^2 = 64 $$

Answer:

64