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 b 3
7. (xy3)(x2yz3)3
2.
c4/c3
a4b2c3/abc
3.
(42 x 32)2
9.
4.
(a3b2)(a2b)
10. 4a3b4/2ab
5.
(x2y3)2
11. (a6b2)6
6.
B2 x aB2
12. 2a2 x a4
8.
a2b2/a2b2
Negative
Exponents
-1
“a ”
Equations like
is the same
as “1/a”.
Example:1) 2-2
=1/22 =1/4
-4
2) 3
4
=1/3 =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
2)82/3
=3√82
=3√64
=√27
=4
Activity
Express each with positive exponents.
1. 91/2
2.
9-1/2
3.
(a/b)-1/2
4.
(x2y3)1/4