Question

simplify. write final answer without negative exponents.

\\(\frac{4x^{\frac{1}{2}}}{x}\\)

\\(\circ\\ \frac{2}{x^{\frac{1}{2}}}\\)
\\(\circ\\ 4x^{\frac{3}{2}}\\)
\\(\circ\\ \frac{4}{x^{\frac{1}{2}}}\\)
\\(\circ\\ 2x^{\frac{1}{2}}\\)

Explanation:

Identify the given expression

Using the Properties of Exponents knowledge point

$$ \frac{4x^{\frac{1}{2}}}{x} $$

Apply exponent rules to simplify

Using the Properties of Exponents knowledge point

$$ \frac{4x^{\frac{1}{2}}}{x^1} = 4x^{\frac{1}{2} - 1} = 4x^{-\frac{1}{2}} $$

Rewrite with positive exponents

Using the Negative Exponent Rule knowledge point

$$ 4x^{-\frac{1}{2}} = \frac{4}{x^{\frac{1}{2}}} $$

Answer:

• (A) \(\frac{2}{x^{\frac{1}{2}}}\)
• (B) \(4x^{\frac{3}{2}}\)
• (C) \(\frac{4}{x^{\frac{1}{2}}}\) (Correct answer)
• (D) \(2x^{\frac{1}{2}}\)