Cand ai inmultire cu aceeasi baza, exponentii se aduna a^m * a^n = a^(m+n)
Cand ai impartire cu aceeasi baza, exponentii se scad a^m : a^n = a^(m-n)
Can ai o relatie de forma (a^m)^n = a^(m*n)
f) (125:125)/5 = 1/5
l) [25⁵*(5⁻²)⁴]/5³ = [(5²)⁵ * 5⁻⁸]/5³ = [5¹⁰ * 5⁻⁸]/5³ = 5⁷* 5⁻⁸ = 5⁻¹ = 1/5
m) 2²⁵/(4³ * 8⁶) = 2²⁵/(2⁶ * 2¹⁸) = 1/(2⁶*2⁷) = 1/2¹³
4 se poate scrie ca 2² si 8 ca 2³
n) (18 * 9⁵)/3¹² = (2*3² * 3¹⁰)/3¹² = (2*3¹²)/3¹² = 2
18 = 3²* 2
9⁵ = (3²)⁵ = 3¹⁰
o) 125⁵ = (5³)⁵ = 5¹⁵
25⁴ = (5²)⁴ = 5⁸
(5¹⁵ * 5⁵)/5⁸ = 5⁷ * 5⁵ = 5¹²
p) 4⁻² = (2²)⁻² = 2⁻⁴
16² = (2⁴)² = 2⁸
=> (2⁻⁴ * 2⁸)/2⁶ = 2⁻⁴ * 2² = 2⁻² = (1/2)² = 1/4
q) (3⁶+3⁹ -1)/(9² * 3) = (729 + 19683 -1) / (3⁴ * 3) = 20411 /3⁵ = 20411/243
r) 4¹³ = (2²)¹³ = 2²⁶
16³= (2⁴)³ = 2¹²
=> (2²⁶ * 2⁻¹⁰)/2¹² = 2¹⁴ * 2⁻¹⁰ = 2⁴ = 16
