How to Use Properties of Rational Exponents
Rational exponents are exponents that are in the form of "a/b." Problems with these kinds of exponents can be difficult to solve unless you have a scientific or engineering calculator. Even with a calculator they can be difficult to input properly. Rational exponents, however, can be rewritten in radical form. By combining this property with the properties that apply to all exponents, these problems can be simplified and solve directly or at least with minimal calculator input errors.
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Instructions
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1
Evaluate the portions of the problem that represent a power raised to a power. This property applies to integer as well as rational exponents.
Example:
(x^2 * y^3/2)^2 = x^(2*2) y^(3/2 * 2) = x^4 * y^3 -
2
Evaluate the portions of the problem that involve multiplication of two exponent expression that have the same base. This property applies to both integer and rational exponents.
Example:
x^2/3 * x^1/3 = x^(2/3 + 1/3) = x^1 = x -
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3
Evaluate the portions of the problem with negative exponents. This step may be done at any time to help simplify the other steps, if necessary.
Example:
x^2/3 * y^-2/3 = (x^2/3)/(y^2/3) = (x/y)^2/3 -
4
Convert rational exponents to radical, or root, form. Examples of radical form include "the square root of x" or "the fifth root of y."
Example:
(x/y)^2/3 = the cube root of (x/y)^2 -
5
Combine the steps to solve a more complex problem. Several examples are provided in the links at the bottom of this page.
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