Simplify Powers: 2^4 × 2^-2 × 2^3 Using Exponent Rules

Question

Reduce the following equation:

$2^4\times2^{-2}\times2^3=$

00:00 Simplify the following problem

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

00:06 equals the same base raised to the sum of the exponents (N+M)

00:10 We will apply this formula to our exercise

00:14 Note that we are adding a negative factor

00:19 A positive x A negative is always negative, so we perform a subtraction

00:28 Let's continue to solve the problem

00:38 This is the solution

To solve this problem, we'll apply the rule for multiplying powers with the same base:

Step 1: Recognize that all terms share the base 2.
Step 2: Apply the multiplication rule for exponents: $2^m \times 2^n = 2^{m+n}$ .
Step 3: Combine the exponents: $2^{4} \times 2^{-2} \times 2^{3}$ becomes $2^{4 + (-2) + 3}$ .

According to the provided choices, the reduced expression using the property is $2^{4-2+3}$ , which aligns with choice 1.

$2^{4-2+3}$