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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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EXPONENTS

VAL JOSEPH DE GUZMAN


Laws of Exponents


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

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

It is in the form “(an)m”.

Solution:anm

Example:(32)4

=32(4)

=38

=6561


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

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


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


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


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


Activity

Express each with positive exponents.

  • 91/2

  • 9-1/2

  • (a/b)-1/2

  • (x2y3)1/4


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