1. Exponents and Radicals Digital Lesson

2. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Repeated multiplication can be written in exponential form. Definition: Exponents exponent 3434 base

3. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 3 Properties of Exponents For all real numbers a and b and all integers m and n,

4. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 4 Properties of Exponents Continued For all real numbers a and b and all integers m and n,

5. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 5 Properties of Exponents Continued For all real numbers a and b and all integers m and n,

6. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 6 Scientific Notation Scientific notation is a convenient way to write very large or very small numbers. integer a.) -3.683 x 10 7 = -36830000. 7 decimal places b.) 0.495 x 10 -5 = 0.00000495 5 decimal places Example:

7. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 7 Definition of nth Root A square root of a number is one of its two equal factors. A cube root of a number is one of its three equal factors. nth root of a

8. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 8 Definition: Principal Root The principal nth root of a is the nth root that has the same sign as a. radical symbol radicand index 3 is the principal 4th root of 81. 5 is the principal cube root of 125.

9. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 9 Properties of Radicals For all real numbers a and b and all positive integers m and n,

10. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 10 Properties of Radicals Continued For all real numbers a and b and all positive integers m and n, 6. If n is even, If n is odd,

11. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 11 Rationalizing Denominators Example: Rationalize the denominator. rationalizing factor conjugate simplified

12. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 12 Rational Exponents rational exponent Example: Simplify the radical expression.

13. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 13 Simplifying Radicals An expression involving radicals is in simplest form when the following are satisfied. 1. All possible factors have been removed from the radical. 2. The denominators have been rationalized. 3. The index of the radical is reduced.