Expand (2 × 3)³ using laws of exponents 

To expand \((2 \times 3)^3\) using the laws of exponents, follow these steps:

### Step 1: Recognize the multiplication inside the parentheses.
\[
(2 \times 3)^3
\]

### Step 2: Apply the exponent to each factor inside the parentheses.
According to the **power of a product rule**, \((ab)^n = a^n \times b^n\), we can expand:
\[
(2 \times 3)^3 = 2^3 \times 3^3
\]

### Step 3: Calculate the exponents.
Now, compute each term:
\[
2^3 = 2 \times 2 \times 2 = 8
\]
\[
3^3 = 3 \times 3 \times 3 = 27
\]

### Step 4: Multiply the results.
Finally, multiply the two results together:
\[
8 \times 27 = 216
\]

So, \((2 \times 3)^3 = 216\).

Would you like further details or have any questions?

### Related Questions:
1. What is the result of \((4 \times 5)^2\) using the same method?
2. How do you apply the power of a quotient rule to \(\left(\frac{2}{3}\right)^3\)?
3. What is the value of \(2^4 \times 3^4\)?
4. How does the law of exponents apply to \((a \times b)^n\)?
5. Can you expand \((2 \times 5)^4\) using laws of exponents?

### Tip:
Always break down expressions inside parentheses before applying exponents to make calculations easier.

Learn how to expand (2 × 3)³ using the laws of exponents with a detailed step-by-step solution. This problem covers key concepts in exponents, including the power of a product rule. Suitable for students in Grades 7-9.

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