What is what to do when dividing exponents?

When dividing exponents with the same base, you subtract the exponents. This rule is a fundamental concept in Exponent Rules.

Here's the breakdown:

• The Rule: x^m / xⁿ = x^(m-n)

• Explanation:

  • You have the same base, 'x', raised to different powers, 'm' and 'n'.
  • To divide, you keep the base the same and subtract the exponent in the denominator ('n') from the exponent in the numerator ('m').

• Example:

  • 2⁵ / 2² = 2^(5-2) = 2³ = 8

• Important Notes:

  • The base MUST be the same for this rule to apply. You cannot directly simplify expressions like 3⁴ / 5² using this rule.
  • Pay attention to negative exponents: subtracting a negative exponent becomes addition. For instance, x³ / x^-2 = x^{(3 - (-2))} = x⁵
  • A good grasp of Negative Exponents is useful when working with dividing exponents.
  • If the exponent in the denominator is larger than the exponent in the numerator, you'll end up with a negative exponent, which can be further simplified (using the rule for negative exponents).
  • Any number (except 0) raised to the power of 0 is 1. (x⁰ = 1 when x ≠ 0). So, if your division results in an exponent of 0, the entire expression simplifies to 1. This is related to Zero Exponent.