How to Calculate the Square Root as a Fraction of a Power

Written by william nagel
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Exponential notation allows you to express repeated multiplication in shorthand. For example, 2 x 2 x 2 expressed with exponential notation becomes 2^3. Exponential notation can also be used to express square roots and other radicals as fractional exponents. Expressing a root as a fractional exponent helps simplify equations, making them easier to reduce, and is a valuable tool for solving equations in algebra and calculus.

Skill level:


  1. 1

    Examine the root (√) symbol, called the "radical." The number "a" beneath the radical is the "radicand." The number "n" nested in the "v" shape on the outside of the radical symbol is the "index." If the radical does not have an index, it is a square root and the index is assumed to be 2.

  2. 2

    Remove the radicand from beneath the radical. The radicand "a" becomes the base "a" of your exponential expression. It does not change.

  3. 3

    Take the index "n" and raise the base "a" to the (1/n) power. In the case of a square root, the expression becomes a^(1/2). The index "n" becomes the denominator of your fractional exponent.

  4. 4

    Simplify your expression. You can manipulate your fractional exponent like any other exponential expression.

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