Question

\sqrt{6p}

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Apply the rational exponent rule

The square root of a term is equivalent to raising that term to the power of \( \frac{1}{2} \).

$$ \sqrt{x} = x^{\frac{1}{2}} $$

Applying this to the expression:

$$ \sqrt{6p} = (6p)^{\frac{1}{2}} $$

Step 2: Distribute the exponent

Apply the power of a product rule, \( (ab)^n = a^n b^n \):

$$ (6p)^{\frac{1}{2}} = 6^{\frac{1}{2}} p^{\frac{1}{2}} $$

Answer:

$$ (6p)^{\frac{1}{2}} \text{ or } 6^{\frac{1}{2}} p^{\frac{1}{2}} $$