less than a minute read Jun 17, 2024

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)

  1. Identify the base: The base is 'x' in both terms.
  2. Identify the exponents: The exponents are 12 and -6.
  3. Apply the product of powers rule: Add the exponents: 12 + (-6) = 6.
  4. 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.

Featured Posts