For details on it including licensingclick here. This book is licensed under a Creative Commons by-nc-sa 3. See the license for more details, but that basically means you can share this book as long as you credit the author but see belowdon't make money from it, and do make it available to everyone else under the same terms. This content was accessible as of December 29,and it was downloaded then by Andy Schmitz in an effort to preserve the availability of this book.

Each type of exponent has a specific meaning. Rational exponents combine powers and roots of the base, and negative exponents indicate that the reciprocal of the base is to be used. Here are some examples of the kinds of numbers we'll be working with: The laws of exponents Let's use some numerical examples, all powers of two because they're convenient, to derive the most important laws of exponents.

Now let's multiply numbers with the same base: The rule for multiplying powers of a common base is We just add exponents. Look back at the example and make sure you understand why.

Now division, again with powers of two: So to divide powers of the same base, we just subtract exponents. And finally, let's raise a power to a power: To raise a power to a power, simply multiply exponents: Here is a table of the laws of exponents.

Tap it to download a copy for your notes.

Negative exponents Let's begin with the exponent It means "take the reciprocal. Now we can use the power law of exponents to extend that property to any negative exponent.

For example, here are two ways of looking at x Both lead to the same result. You will find that you have a lot of freedom about how to use negative exponents when you work problems.

There will usually be a couple of ways to get a solution. The general formula for a negative exponent is thus In the examples that follow, the idea will be to rewrite each expression so that it has no negative exponents. In these examples I'll take meticulous steps.

I hope you'll eventually learn how to cut some corners, but for now, seeing these problems done in great detail might be helpful.

Try to follow and understand the logic behind each step.Simplify each Expression (variable exponents) a) (xb 1)3(xb 4) 2 b) (a2)m+2(a3)4m c) 5a2tb 3t 3 Reduce and Rewrite each expression using a single radical sign. a) 3 p 3 p 2 b) p 5 3 p 4 c) 3 q p 5x; d) 5a 3 p 2a; Answers a) 6 p 72; b) 6 p ; c) 6 p 7; d) 9 p 2a; Solve the rational exponent problems for x.

a) 4x1=3 = 20 b) 3x1=4. Rewrite the expression using rational exponent notation. Do not simplify. 1. 40 6 15 2 2. 3. 9 3 4 Use the properties of rational exponents to simplify WITHOUT USING A CALCULATOR. If possible, leave your answer as a Simplify the expression using the properties of radicals.

If possible, leave your answer as a simplified radical. Demonstrates how to simplify fractions containing negative exponents. Provides worked examples, showing how the same exercise can be correctly worked in more than one way.

Warns against confusing "minus" signs on numbers and "minus" signs in exponents. How do you rewrite with rational exponents: square root 11?

Algebra Exponents and Exponential Functions Fractional Exponents. 1 Answer George C. Jun 18, Answer: #sqrt(11) = 11^(1/2 How do you simplify fractional exponents? In order to evaluate fractional exponents, we can express them using the following relationship: In this formula, represents the index of the radical from the denominator of the fraction and is the exponent .

Can some one help me with these two problems multiply and simplify by factoring ∜*∜ type exact answer, using radicals as needed 2) Rewrite with rational exponents (ã3mn)^3 the (mn) are included under the square root as well.

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Rewrite the rational exponent as a radical by extending the properties of