Question

which expression is equivalent to \\(\frac{15a^6b^4}{5a^2b}\\)?

\\(10a^4b^4\\)

\\(3a^4b^3\\)

\\(3a^2b^4\\)

\\(10a^4b^3\\)

Explanation:

Identify the given expression

We are given the rational expression:

$$ \frac{15a^6b^4}{5a^2b} $$

Our goal is to simplify this expression by dividing the coefficients and applying exponent rules to the variables.

Simplify the numerical coefficients

Using the Rational Expressions knowledge point

$$ \frac{15}{5} = 3 $$

Simplify the variable a

Using the Rational Expressions knowledge point

$$ \frac{a^6}{a^2} = a^{6-2} = a^4 $$

Simplify the variable b

Using the Rational Expressions knowledge point

$$ \frac{b^4}{b^1} = b^{4-1} = b^3 $$

Combine the simplified parts

Using the Rational Expressions knowledge point

$$ 3 \cdot a^4 \cdot b^3 = 3a^4b^3 $$

Answer:

• (A) \(10a^4b^4\)
• (B) \(3a^4b^3\) (Correct answer)
• (C) \(3a^2b^4\)
• (D) \(10a^4b^3\)