## Understanding the Multiplication of Exponents: (x^a)(x^b)

When multiplying exponents with the same base, we can simplify the expression using a simple rule. This rule states that we **add the exponents** while keeping the base the same.

### The Rule

** (x^a)(x^b) = x^(a+b)**

This rule is based on the fundamental understanding of exponents. For example:

**x^a**means multiplying x by itself 'a' times.**x^b**means multiplying x by itself 'b' times.

Therefore, **(x^a)(x^b)** is simply multiplying x by itself (a+b) times.

### Example:

Let's take a simple example:

**(x^3)(x^2) = x^(3+2) = x^5**

**x^3**is equal to x * x * x**x^2**is equal to x * x- Therefore,
**(x^3)(x^2)**is equal to (x * x * x) * (x * x) =**x^5**

### Applying the Rule:

This rule can be applied to any exponents with the same base, whether they are integers, fractions, or even variables. For example:

**(y^2)(y^5) = y^(2+5) = y^7****(a^(1/2))(a^(3/2)) = a^(1/2 + 3/2) = a^2****(m^n)(m^p) = m^(n+p)**

### Conclusion:

The rule for multiplying exponents with the same base is a fundamental concept in algebra. Understanding this rule allows us to simplify complex expressions and work with exponents more efficiently.