What is what to do with exponents when dividing?

When dividing terms with exponents that have the same base, you subtract the exponents. This rule is a fundamental concept in working with Exponents.

Here's the rule:

x^m / xⁿ = x^(m-n)

Explanation:

• Same Base: This rule only applies if the bases (the 'x' in the above example) are the same. You can't directly apply this rule to something like 2³ / 3².

• Subtracting Exponents: You subtract the exponent in the denominator (n) from the exponent in the numerator (m).

Examples:

• 5⁷ / 5³ = 5^(7-3) = 5⁴

• x¹⁰ / x² = x^(10-2) = x⁸

Important Considerations:

• Zero Exponents: If m = n, then x^(m-n) = x⁰, which equals 1 (as long as x is not zero). See also Zero%20Exponent.

• Negative Exponents: If n > m, then x^(m-n) will result in a negative exponent. A negative exponent means you take the reciprocal of the base raised to the positive version of that exponent. For example, x^-2 = 1/x². More on Negative%20Exponents.

• Fractions: The rule still applies if the exponents are fractions. For example, x^(1/2) / x^(1/4) = x^{(1/2 - 1/4)} = x^(1/4)

• Combining with other rules: You may need to combine this rule with other exponent rules like the power of a product rule or the power of a power rule when simplifying expressions. See also Exponent%20Rules for more information.