Index Laws Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations.

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Presentation transcript:

Index Laws Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations are called the “Index Laws” b x b = basex = exponent

Index Laws

Other Properties of Exponents Any single number or variable is always to the first power

Basic Examples

More Examples

nth Roots An nth root of number a is a number whose nth power is a. a number whose nth power is a If the index n is even, then the number a must be nonnegative. is not a real number

Square Root of x 2 Page 393

When n Is Even

Exponent 1/n When n Is Odd

Rational Exponents

Evaluating in Either Order

Negative Rational Exponents

Evaluating a -m/n

Rules for Rational Exponents 7-6

Simplifying

Simplifying

Simplifying

Multiplying Radicals – Different Indices

Different Indices

Rational Exponents Eliminate the root, then the power

Eliminate the Root, Then the Power

Negative Exponents

Eliminate the root, then the power

Negative Exponents Eliminate the root, then the power

Using the index templates on your CAS calculator:

No Solution Eliminate the root, then the power