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How to Algebraically Manipulate an Exponent

Exponents represent how many times a number or variable, called the base, should be multiplied by itself. For example, 3^5 is equal to 3 * 3 * 3 * 3 * 3 and x^3 is equal to x * x * x. The mathematical opposite of exponents are roots. To cancel out an exponent from an equation, take the equivalent root of both sides of the equation. For example, a square root is equivalent to an exponent of 2 and a cube root is equivalent to an exponent of 3.

Instructions

- 1
  Combine exponents when two like bases are multiplied by adding together the exponents, which is represented by the formula x^a * x^b = x^(a + b). Combine 3^2 * 3^3 for practice: 3^(2 + 3) = 3^5. Apply the variable: 3^5 = 243.
- 2
  Combine the exponents of like bases in a ration, or division, by subtracting the exponent of the denominator from the exponent of the numerator as represented in the formula (x^a) / (x^b) = x^(a - b). Combine (x^6) / (x^3) for practice: x^(6 - 3) = x^3. Note that this is the simplified version of the expression.
- 3
  Apply an exponent that's outside a parenthesis to each term within: for example, (xy)^3 = x^3 * y^3. Multiply the exterior exponent to any interior exponents: for example, (x^5)^2 = x^(5 * 2) = x^10.

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