Question

Usando as propriedades que aprendeu deixe as potências em uma só base, sem resolvê-las. a) 71^3 . 71^6 = ______ b) 3^3 . 3^- 4 = ____ c) 7^- 8 . 7^6 = ____ d) 2^15 : 2 = ____ e) 18^1 : 18^3 = _____ f) 1^9 : 1 = ________ g) (5^7 )^6 = ______ h) (9^9 )^6 = _______ i) (- 4^2 )^0 = _____ j) 6^19 : 6^11 = _______

Answer 1

a) $71^3\cdot71^6=71^{3+6}=71^9$

b) $3^3\cdot3^{-4}=3^{3-4}=3^{-1}$

c) $7^{-8}\cdot7^6=7^{-8+6}=7^{-2}$

d) $2^{15}:2=2^{15}:2^1=\dfrac{2^{15}}{2^1}=2^{15-1}=2^{14}$

e) $18^1:18^3=18^{1-3}=18^{-2}$

f) $1^9:1=1^{9-1}=1^8=1$

g) $\left(5^7\right)^6=5^{7\cdot6}=5^{42}$

h) $\left(9^9\right)^6=9^{9\cdot6}=9^{54}$

i) $\left(-4^2\right)^0=-4^{2\cdot0}=-4^0=1$

j) $6^{19}:6^{11}=6^{19-11}=6^8$