## Simplifying Exponents: (x^3)^3 = x^n

In mathematics, understanding exponent rules is crucial for simplifying expressions and solving equations. One common rule involves raising a power to another power, like in the expression **(x^3)^3 = x^n**. Let's break down how to determine the value of 'n'.

### Understanding the Rule

The rule for simplifying expressions of this form is: **(x^m)^n = x^(m*n)**. This means that when raising a power to another power, we multiply the exponents together.

### Applying the Rule

In our example, (x^3)^3, we have m = 3 and n = 3. Applying the rule, we get:

(x^3)^3 = x^(3*3) = **x^9**

Therefore, **n = 9**.

### Example

Let's consider another example: **(y^2)^5 = y^n**.

- Applying the rule: (y^2)^5 = y^(2*5) =
**y^10** - Therefore,
**n = 10**.

### Importance

Understanding this rule is essential for various mathematical operations, including:

**Simplifying algebraic expressions****Solving exponential equations****Working with scientific notation**

By consistently applying the rule, you can efficiently simplify complex expressions involving exponents and solve a wider range of mathematical problems.