Simplify the Exponential Expression: 11^(5a) ÷ 11^(a-4)

To solve the problem $\frac{11^{5a}}{11^{a-4}}$, we need to use the Power of a Quotient Rule for exponents, which states that $\frac{b^m}{b^n} = b^{m-n}$.

Let's apply this rule to the given expression:

• The base is $11$, which is the same for both the numerator and the denominator.
• The exponent in the numerator is $5a$.
• The exponent in the denominator is $a - 4$.

According to the formula $\frac{b^m}{b^n} = b^{m-n}$, we can subtract the exponent in the denominator from the exponent in the numerator:

$5a - (a - 4) = 5a - a + 4$.

This simplifies to $4a + 4$.

Therefore, $\frac{11^{5a}}{11^{a-4}} = 11^{4a + 4}$.

The correct answer provided was $11^{4a-4}$.

Therefore, the final expression we arrived at using the Power of a Quotient Rule is: $11^{4a + 4}$.

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