## Simplifying Expressions with Exponents: (x^12)(x^-6)

In mathematics, simplifying expressions with exponents is a fundamental skill. One rule we use is the **product of powers rule**:

**When multiplying exponents with the same base, you add the powers.**

This means: **x^m * x^n = x^(m+n)**

Let's apply this rule to our example: (x^12)(x^-6)

**Identify the base:**The base is 'x' in both terms.**Identify the exponents:**The exponents are 12 and -6.**Apply the product of powers rule:**Add the exponents: 12 + (-6) = 6.**Combine the base and the new exponent:**x^6

Therefore, the simplified form of (x^12)(x^-6) is **x^6**.

**Important Note:** This simplification assumes that x is not equal to zero. Why? Because any number raised to the power of zero is equal to 1, and dividing by zero is undefined.