Question

Preciso de ajuda nesse 1

Answer 1

Para a realização desses exercícios, vamos utilizar as seguintes regras de potenciação:

• $a^m\cdot a^n=a^{m+n}$
• $\frac{a^m}{a^n} =a^{m-n}$
• $(a^m)^n=a^{m\cdot n}$
• $a^m\cdot b^m=(a\cdot b)^m$

a) $8^5\cdot8^9=8^{5+9}=8^{14}$

b) $8^5\cdot8^{12}\cdot\frac{8^{-9}}{8^6}=8^5\cdot8^{12}\cdot8^{-15}=8^{5+12-15}=8^2$

c) $x^{-5}\cdot x^{-2}\cdot\frac{x^{12}}{x^6}=x^{-5}\cdot x^{-2}\cdot x^6=x^{-5-2+6}=x^{-1}$

d) $4^7\cdot5^7=(4\cdot5)^7=20^7$

e) $\frac{x}{x^6}=x^{1-6}=x^{-5}$

f) $(x^{-5})^3=x^{(-5)\cdot3}=x^{-15}$

g) $y^{-1}\cdot y^{-11}\cdot\frac{y^{15}}{y^{26}}=y^{-1}\cdot y^{-11}\cdot y^{-11}=y^{-1-11-11}=y^{-23}$