Simplify the Expression: 4^5 × 4 × 4^2 Using Exponent Rules

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 Any number raised to the power of 1 is always equal to itself

00:06 We'll apply this formula to our exercise, and raise it to the power of 1

00:12 According to the laws of exponents, the multiplication of powers with an equal base (A)

00:17 equals the same base raised to the sum of the exponents (N+M)

00:24 We'll apply this formula to our exercise

00:28 We'll maintain the base and proceed to add up the exponents

00:34 This is the solution

Step-by-Step Solution

To solve this simplification problem, we will apply the rules of exponents. Our steps are as follows:

Step 1: Identify the exponents of the base. We have $4^5$ , $4^1$ (since $4$ is equivalent to $4^1$ ), and $4^2$ .
Step 2: Use the property of exponents: $a^m \times a^n = a^{m+n}$ to combine powers of the same base.
Step 3: Calculate the sum of the exponents: $5 + 1 + 2 = 8$ .
Step 4: Express the simplified result in the form of a single power of 4: $4^{8}$ .

Therefore, the expression $4^5 \times 4 \times 4^2$ simplifies to $4^{5+1+2}$ , which further simplifies to $4^8$ .

Checking the multiple-choice options, the correct choice is: $4^{5+1+2}$ , aligning with our solution.