How to Distribute Exponents


Exponents are written in superscript and basically refer to repeated multiplication. An understanding of distributing exponents is necessary for algebra courses, trigonometry, calculus and more advanced mathematics courses. The following explanation will use the example problem of ((6+3)x ^1/2 + 4y^2 + z^0)^3.

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  • Simplify operations that are within parentheses. In the example, add the 6 and 3. This results in (9 x ^1/2 + 4y^2 + z^0)^3.

  • Simplify the exponents within the parentheses. In this example, the z^0 can be simplified to 1, since any value to the zero power equals 1. The result is (9x^(1/2) + 4y^2)^3.

  • Distribute the exponents outside of the parentheses to the inside terms. In this example, the exponents are distributed as follows: 9^3 x^(1/2 3) + 4^3 y^(2 3). The 9^3 can be simplified by multiplying the 9 by itself 3 times, which results in 729, and the 4 by itself 3 times, which results in 64. The final result is 729x^(3/2) + 64y^6.


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