Forum - - exponents

# - exponents

exponentiations

 Exponentiation is  written as bn, involving two numbers, the base b and the exponent  n. When n is a positive integer, exponentiation corresponds to repeated multiplication; in other words, a product of n factors, each of which is equal to b (the product itself can also be called power): $b^n = \underbrace{b \times \cdots \times b}_n$  b0 =  1                                                        b1 =  a

example

3 5  = 3 · 3 · 3 · 3 · 3 = 243

exercise

 32 015 23 (-1)18 (32)3 (-1)13 (-5)2 (-18)3 90 (1)13

multiplaying powers

 powers with same exponents  a  and b two non zero rationnals  m   a   positif integer anx bn = ( axb) n powers with same bases  a  is non zero rationnal  m and  n  two  positif integers amx an =  am+n the sign of power * the power is negative when the base is negative and  the exponent in an odd number                          * the power is positive when the base is negative and the exponent in an even number                         * the power is positive when the base is positive when the base is power  x is a positive non zero integer  m and  n  two  positif integers $\ (x^m)^n=x^{mn}$

example

symplify

1)            (2a4)x(5a7)

2)                  (2a5)3

exercises

1)   prove that

814 = 98
3212 = 260.

2)   find the negative powers

37 ; (-3)17 ; (-3)12 ; -39 ; -312