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How to Combine Variables With Different Exponents

In algebra, an exponent represents how many times a number or variable, called the base, should be multiplied by itself. For example, x^4 equals x * x * x * x and 3^2 equals 3 * 3. Exponents can be whole numbers, negative numbers, fractions or variables. All non-negative exponents follow the same basic rules but exponents other than whole numbers may also have specific rules for that type of operation.

Instructions

- 1
  Perform the multiplication between two like bases with different exponents by keeping the same base and adding the exponents. This is represented by the formula x^a * x^b = x^(a + b). For example, x^8 * x^4: x^(8 + 4) = x^(12).
- 2
  Divide like bases with different exponents by keeping the base and subtracting the denominator exponent from the numerator exponent. This is represented by the formula (x^a) / (x^b) = x^(a - b). For example, (x^6) / (x^2) : x^(6 - 2) = x^4.
- 3
  Note that variables with different exponents cannot be added to or subtracted from each other. For example, 3x^2 - 2x^3 cannot be combined; the expression is already in its simplified form.

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