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

Simplify the following equation:

$$$4^5\times4\times4^2=$

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.