Simplify the Expression: 6^(4x) ÷ 6^(x+1)

To solve the given expression $\frac{6^{4x}}{6^{x+1}}$, we must apply the Power of a Quotient Rule for Exponents. This rule states that $\frac{a^m}{a^n} = a^{m-n}$.

Using this rule, the given expression can be rewritten as follows:

• The numerator is $6^{4x}$.
• The denominator is $6^{x+1}$.

Apply the Power of a Quotient Rule:

$\frac{6^{4x}}{6^{x+1}} = 6^{4x - (x + 1)}$

We need to simplify the exponent by performing the subtraction $4x - (x + 1)$:

Step 1: Distribute the subtraction sign to the terms inside the parenthesis:

• $4x - x - 1$

Step 2: Combine like terms:

• $3x - 1$

The expression simplifies to:

$6^{3x-1}$

Therefore, the solution to the question is: $6^{3x-1}$.