Question

question 10 (1 point)

when fully simplified, excluding restrictions, \\(\frac{24x^5}{2x} \times \frac{x^3}{6x^2}\\) is equal to

a) \\(\frac{2}{x^5}\\)

b) \\(132x^3\\)

c) \\(\frac{24x^8}{12x^3}\\)

d) \\(2x^5\\)

Explanation:

Multiply the numerators and denominators

$$ \frac{24x^5}{2x} \times \frac{x^3}{6x^2} = \frac{24x^5 \cdot x^3}{2x \cdot 6x^2} = \frac{24x^8}{12x^3} $$

Simplify the coefficients and exponents

$$ \frac{24}{12} = 2 $$

$$ \frac{x^8}{x^3} = x^{8-3} = x^5 $$

Combine the simplified terms

$$ 2 \cdot x^5 = 2x^5 $$

Answer:

• A) \(\frac{2}{x^5}\)
• B) \(132x^3\)
• C) \(\frac{24x^8}{12x^3}\)
• D) \(2x^5\) (Correct answer)