Math 9 - Exponent Laws I: Multiplying and Dividing Powers - Free Printable

The image shows a math lesson on multiplying powers with the same base. Let's break down the problem and explain the solution step by step.

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🔹 Problem:

$$
2^2 \times 2^3
$$

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🔹 Step-by-Step Explanation:

#### Step 1: Understand what the exponents mean
- $2^2$ means $2 \times 2 = 4$
- $2^3$ means $2 \times 2 \times 2 = 8$

So, multiplying them:
$$
2^2 \times 2^3 = (2 \times 2) \times (2 \times 2 \times 2)
$$

Now combine all the factors:
$$
2 \times 2 \times 2 \times 2 \times 2 = 2^5
$$

So,
$$
2^2 \times 2^3 = 2^5
$$

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🔹 General Rule:

When you multiply powers with the same base, you add the exponents:
$$
a^m \times a^n = a^{m+n}
$$

In this case:
$$
2^2 \times 2^3 = 2^{2+3} = 2^5
$$

✔ This is the key rule being taught in the image.

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✔ Final Answer:

$$
2^2 \times 2^3 = 2^5
$$

This demonstrates that when multiplying powers with the same base, we add the exponents.

Let me know if you'd like to see examples with variables or more complex expressions!