Question

carl simplified this expression. what did he most likely do wrong?
\\(\frac{6a^2b^3}{2ab} = \frac{6ab^5}{2ab} = 3ab^4\\)
options:
he did not divide both sides by 2ab.
he used a law of exponents on factors with different bases.
he did not divide by 2ab.
nothing, because \\(3ab^4\\) is correct.

Explanation:

Step1: Analyze the original expression simplification

The original expression is \(\frac{6a^{2}b^{3}}{2ab}\). When simplifying, we should use the quotient rule of exponents (\(\frac{x^{m}}{x^{n}}=x^{m - n}\)) for like bases. But Carl changed the numerator from \(6a^{2}b^{3}\) to \(6ab^{5}\), which is incorrect. He seems to have applied exponent rules to different - base factors (he modified the exponents of \(a\) and \(b\) in a wrong way, maybe treating different - base terms as same - base terms for exponent operations).

Step2: Evaluate each option

• Option 1: He did divide by \(2ab\) in the second step, so this is wrong.
• Option 2: He used a law of exponents (probably the quotient rule or product rule) on factors with different bases (he incorrectly modified the exponents of \(a\) and \(b\) in the numerator, treating them as if they can be combined in a wrong way, which is like using exponent laws on different - base factors). This option is correct.
• Option 3: He did divide by \(2ab\), so this is wrong.
• Option 4: The simplification is incorrect because the numerator was wrongly modified, so this is wrong.

Answer:

He used a law of exponents on factors with different bases.