Rational exponents - A complete course in algebra.
Given an expression with a rational exponent, write the expression as a radical. Determine the power by looking at the numerator of the exponent. Determine the root by looking at the denominator of the exponent. Using the base as the radicand, raise the radicand to the power and use the root as the index.
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Simplify radical expressions. The properties of exponents,. These properties can be used to simplify radical expressions. A radical expression is said to be in its simplest form if there are.. The product of two conjugates is always a rational number which means that you can use conjugates to rationalize the denominator e.g.
Simplifying radical expressions, rational exponents, radical equations 1. 5.6 Simplifying Radicals 2. Definitions A perfect square is the square of a natural number. 1, 4, 9, 16, 25, and 36 are the first six perfect squares. A perfect cube is the cube of a natural number.
Fractional exponents allow greater flexibility (you'll see this a lot in calculus), are often easier to write than the equivalent radical format, and permit you to do calculations that you couldn't before. For instance.
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Writing a Rational Expression in Lowest Terms. A rational expression is a fraction where the numerator and the denominator are polynomials. Reducing a rational expression to lowest terms is similar to reducing an arithmetic fraction to lowest terms.