catherine simplifies 6^a x 6^3/6^b to 6^(a-3+b).
Justin simplifies the same expression but gets a different answer, 6^(a+3)-6
Who is correct?
To simplify 6^a x 6^3/6^b, you can use the rule of exponentiation that states when you multiply two exponential expressions with the same base, you add their exponents. Dividing two exponential expressions with the same base requires subtracting the exponents.
Applying this rule to the given expression:
6^a x 6^3 / 6^b = 6^(a + 3) / 6^b
Now, we know that:
a + 3 ≠ a - 3 + b
Therefore, Catherine's simplification 6^(a - 3 + b) is not equivalent to the original expression.
On the other hand, Justin's simplification 6^(a + 3) - 6 is also not equivalent to the original expression.
Neither Catherine nor Justin is correct.