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How to Simplify Polynomials With Exponents

Polynomial expressions consist of variables and constants, joined by the four mathematical operations (addition, subtraction, multiplication and division) and raised to positive integer exponents. Simplifying polynomials involves multiplying like variables together and combining like terms.



Like terms are variables raised to the same power. X^2 and x^3 aren't like terms; neither are y^2 and z^2. However, x^2 and 3x^2 are like terms. X^2 and x^3 are like variables, though. The two-step process will simplify any polynomial expression.

Instructions

    • 1

      Consider the expression [a^2bc^3b^2]/[a^(-3)b^5ca]. Combine like variables in the numerator and the denominator. When you multiply like variables together, you add the exponents together. The result will be: [a^2b^3c^3]/[a^(-2)b^5c].

    • 2

      Divide the like variables in the numerator by their counterparts in the denominator. When you divide like variables, you subtract the exponents. After you do this, the example from Step 1 will read a^4c^2/b^2. The reason that b moves to the denominator is that the b-exponent is -2. You could also write the expression as a^4b^(-2)c^2, and it would be equivalent.

    • 3

      Remove any zero-value exponents by treating them as the number 1. Any variable or constant raised to the zero power is equivalent to 1, by definition. So, if you have x^2 in the numerator and the denominator, they cancel each other out.

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