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

Question

Insert the corresponding expression:

64x6x+1= \frac{6^{4x}}{6^{x+1}}=

Video Solution

Solution Steps

00:00 Simply
00:03 According to the laws of exponents, division of exponents with equal bases (A)
00:06 equals the same base (A) to the power of the difference of exponents (M-N)
00:09 Let's use this formula in our exercise
00:12 We'll keep the base, and subtract between the exponents making sure to use parentheses
00:15 negative times positive always equals negative
00:19 Let's group the terms
00:23 And this is the solution to the question

Step-by-Step Solution

To solve the given expression 64x6x+1 \frac{6^{4x}}{6^{x+1}} , we must apply the Power of a Quotient Rule for Exponents. This rule states that aman=amn \frac{a^m}{a^n} = a^{m-n} .

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

  • The numerator is 64x 6^{4x} .
  • The denominator is 6x+1 6^{x+1} .

Apply the Power of a Quotient Rule:

64x6x+1=64x(x+1) \frac{6^{4x}}{6^{x+1}} = 6^{4x - (x + 1)}

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

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

  • 4xx1 4x - x - 1

Step 2: Combine like terms:

  • 3x1 3x - 1

The expression simplifies to:

63x1 6^{3x-1}

Therefore, the solution to the question is: 63x1 6^{3x-1} .

Answer

63x1 6^{3x-1}