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 ”. Solution: a. If n is greater than m use a n-m b. If n is less than m use 1/a n-m Example:2 3 /2 2 =2 3-2 =2

Third Law of Exponents It is in the form “(a n ) m ”. Solution:a nm Example:(3 2 ) 4 =3 2(4) =3 8 =6561

Fourth Law of Exponents If you had encounter an equation like this “(a n b m ) r ”. Solution:a rn b rm Example:(4 3 x 3 2 ) 2 =4 6 x 3 4 =4096 x 81 =331,776

Activity Simplify each of the following. 1.b 2 X b 3 7. (xy 3 )(x 2 yz 3 ) 3 2.c 4 /c 3 8. a 4 b 2 c 3 /abc 3.(4 2 x 3 2 ) 2 9. a 2 b 2 /a 2 b 2 4.(a 3 b 2 )(a 2 b) 10. 4a 3 b 4 /2ab 5.(x 2 y 3 ) (a 6 b 2 ) 6 6.B 2 x aB a 2 x a 4

Negative Exponents

Equations like “a -1 ” is the same as “1/a”. Example:1) 2 -2 =1/2 2 =1/4 2) 3 -4 =1/3 4 =1/81

Activity Transform each equation into an equation with a positive exponent (ab 3 ) -1 2.(3 -2 ) xy -3 3.(1/5) (a+b) -2 (a -2 +b -2 )

Fractional Exponents

An expression like “a n/m ” is the same as the the expression “ m √a n Example:1)3 3/2 =√3 3 =√27 2)8 2/3 = 3 √8 2 = 3 √64 =4

Activity Express each with positive exponents / /2 3. (a/b) -1/2 4. (x 2 y 3 ) 1/4