Reduce the Expression: 4^x × 4^2 × 4^a Using Exponent Laws

Reduce the following equation:

$4^x\times4^2\times4^a=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, the multiplication of exponents with equal bases (A)

00:07 equals the same base raised to the sum of the exponents (N+M)

00:11 We will apply this formula to our exercise

00:15 We'll maintain the base and add the exponents together

00:24 This is the solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Confirm the given expression is $4^x \times 4^2 \times 4^a$ .
Step 2: Apply the exponent rule for multiplication of powers: if $b^m \times b^n = b^{m+n}$ , use this with base 4.
Step 3: Add the exponents of each term.

Let's work through these steps:

Step 1: The expression we have is $4^x \times 4^2 \times 4^a$ .

Step 2: Since all parts of the product have the same base $4$ , we can use the rule for multiplying powers: $4^x \times 4^2 \times 4^a = 4^{x+2+a}$ .

Step 3: The simplified expression is obtained by adding the exponents: $x + 2 + a$ .

Therefore, the expression $4^x \times 4^2 \times 4^a$ simplifies to $4^{x+2+a}$ .