Simplify the Expression: 8³ × 8⁶ Using Laws of Exponents

Simplify the following equation:

$8^3\times8^6=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, the multiplication of exponents with the same base (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

00:16 We will then add up the exponents and raise them to this power

00:19 This is the solution

Step-by-Step Solution

To solve this problem, we'll use the properties of exponents to simplify the expression:

Step 1: Identify the bases and exponents in the expression $8^3 \times 8^6$ .
Step 2: Apply the product of powers property, which states $a^m \times a^n = a^{m+n}$ when the bases are the same.
Step 3: Add the exponents: $3 + 6 = 9$ .

Now, let's work through these steps:

Step 1: Both terms, $8^3$ and $8^6$ , have the same base, 8.

Step 2: According to the product of powers property, we add the exponents: $8^{3+6}$ .

Step 3: Simplifying the exponents gives us $8^9$ .

Therefore, the simplified expression is $8^9$ .