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# Exponents

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### Exponents

1. 1. Powers of Real Numbers(Exponents)<br />
2. 2. Exponents represent repeated multiplication. For example,<br />Introduction <br />
3. 3. More generally, for any non-zero real number a and for any whole number n,<br />Introduction <br />In the exponential expression an, a is called the base and n is called the exponent.<br />
4. 4. a2 is read as ‘a squared’.<br />a3 is read as ‘a cubed’.<br />a4 is read as ‘a to the fourth power’.<br /> ...<br />an is read as ‘a to the nth power’.<br />
5. 5. Caution!<br />
6. 6. Caution!<br />
7. 7. Properties of Exponents<br />
8. 8. Example:<br />
9. 9. Properties of Exponents<br />
10. 10. Example:<br />
11. 11. Properties of Exponents<br />Homework.<br />
12. 12. Example:<br />
13. 13. Some Definitions of Exponents<br />
14. 14. Properties of Exponents<br />Homework.<br />
15. 15. Example:<br />
16. 16. Properties of Exponents<br />Homework.<br />
17. 17. Example:<br />
18. 18. Properties of Exponents<br />Homework.<br />
19. 19. Example:<br />
20. 20. Properties of Exponents<br />All powers of a positive real number a are positive, i.e. for a ∈ R, a > 0, and n ∈ Z,<br />an > 0. <br />2. The even powers of a negative real number a are positive, i.e. for a ∈ R, a ≠ 0 and n ∈ Z,<br />(–a)n = an (if n is an even number).<br />3. The odd powers of a negative real number a are negative, i.e. for a ∈ R, a ≠ 0 and n ∈ Z,<br />(–a)n= –an (if n is an odd number)<br />
21. 21. Example:<br />
22. 22. Example:<br />
23. 23. Properties of Exponents<br /> The terms of an expression which have the same base and the same exponent are called like terms. We can add or subtract like terms.<br />(x ⋅ an) + (y ⋅ an) + (z ⋅ an) = (x + y + z) ⋅ an (a ≠ 0)<br />
24. 24. Example:<br />
25. 25. Let a ∈ R – {–1, 0, 1} <br />(a is a real number other than –1, 0 and 1).<br /> If am = an then m = n.<br />Exponential Equations<br />
26. 26. 2x = 16<br />3x+1 = 81<br />22x + 1 = 8x – 1<br />Examples:<br />
27. 27. Exercises:<br />