Question

Aplicar as propriedades das potencias. (Não resolva as potencias):
a) (6⁸) x ( 6⁴):………..

d) (2 . 4)²: ....................

g) (-3)² . (-3)⁵: ..........................

b) (5.7)³:………….…

e) [(-2)²]³: ....................

h) 3¹⁰ ÷3³: .................................

c) (2/7)⁶ ÷(2/7)⁸: ..................

f) (2)⁷÷(2)-⁴: ...............

i) (5)⁹ ÷(5)⁷: ............................​

Answer 1

Lembre-se que:

$a^m\cdot a^n=a^{m+n}$

Conserva a base e soma os expoentes

$\dfrac{a^m}{a^n}=a^{m-n}$

Conserva a base e subtrai os expoentes

$(a\cdot b)^m=a^m\cdot b^m$

$(a^m)^n=a^{m\cdot n}$

a) $6^8\times6^4=6^{8+4}=6^{12}$

b) $(5\cdot7)^3=5^3\cdot7^3$

c) $\left(\dfrac{2}{7}\right)^6\div\left(\dfrac{2}{7}\right)^8=\left(\dfrac{2}{7}\right)^{6-8}=\left(\dfrac{2}{7}\right)^{-2}$

d) $(2\cdot 4)^2=2^2\cdot4^2$

e) $[(-2)^2]^3=(-2)^{2\cdot3}=(-2)^{6}$

f) $2^7\div2^{-4}=2^{7-(-4)}=2^{7+4}=2^{11}$

g) $(-3)^2\cdot(-3)^5=(-3)^{2+5}=(-3)^7$

h) $3^{10}\div3^3=3^{10-3}=3^7$

i) $5^9\div5^7=5^{9-7}=5^2$