Val joseph de guzman
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EXPONENTS. VAL JOSEPH DE GUZMAN. Laws of Exponents. First Law of exponent. It is in the form “ a n a m ” where both n and m are exponents. Solution: a n+m Example:2 3 (2 2 ) =2 3+2 =2 5 =32. Second Law of Exponents. It is in the form “ a n /a m ”.

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VAL JOSEPH DE GUZMAN

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Val joseph de guzman

EXPONENTS

VAL JOSEPH DE GUZMAN


Val joseph de guzman

Laws of Exponents


First law of exponent

First Law of exponent

It is in the form “anam” where both n and m are exponents.

Solution: an+m

Example:23(22)

=23+2

=25

=32


Second law of exponents

Second Law of Exponents

It is in the form “an/am”.

Solution:

a. If n is greater than m use

an-m

b. If n is less than m use

1/an-m

Example:23/22

=23-2

=2


Third law of exponents

Third Law of Exponents

It is in the form “(an)m”.

Solution:anm

Example:(32)4

=32(4)

=38

=6561


Fourth law of exponents

Fourth Law of Exponents

If you had encounter an equation like this “(anbm)r”.

Solution:arnbrm

Example:(43 x 32)2

=46 x 34

=4096 x 81

=331,776


Activity

Activity

Simplify each of the following.

1.b2 X b3 7. (xy3)(x2yz3)3

2.c4/c3 8.a4b2c3/abc

3.(42 x 32)2 9. a2b2/a2b2

4.(a3b2)(a2b) 10. 4a3b4/2ab

5.(x2y3)2 11. (a6b2)6

6.B2 x aB2 12. 2a2 x a4


Negative exponents

Negative Exponents


Val joseph de guzman

Equations like “a-1” is the same as “1/a”.

Example:1) 2-2

=1/22 =1/4

2) 3-4

=1/34 =1/81


Activity1

Activity

Transform each equation into an equation with a positive

exponent.

1.5-4 5. (ab3)-1

2.(3-2)-3 6. xy-3

3.(1/5)-3 7. (a+b)-2(a-2+b-2)

4.2-1+3-2


Fractional exponents

Fractional Exponents


Val joseph de guzman

An expression like “an/m” is the same as the the expression “ m√an

Example:1)33/2

=√33 =√27

2)82/3

=3√82

=3√64 =4


Activity2

Activity

Express each with positive exponents.

  • 91/2

  • 9-1/2

  • (a/b)-1/2

  • (x2y3)1/4


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