Question

Alguém me ajuda é sobre potenciação

Answer 1

Explicação passo-a-passo:

1.

a) 7² = 49

b) ( -5 )³ = -125

c) ( -2/5 )² = 4/25

d) ( -2,3 )² = 5,29

e) -6² = 36

f) 3⁵ = 243

2.

a) $2^9\cdot \:2^5=2^{9+5}=2^{14}=16384$

b) $1,4^6\cdot \:1,4^4=1,4^{6+4}=1,4^{10}=28,92546\dots$

c) $5^8\cdot \:5^4\cdot \:5=5^{8+4+1}=5^{13}=1220703125$

d) $\frac{3^{10}}{3^7}=3^{10-7}=3^3=27$

e) $\frac{2,7^5}{2,7}=2,7^{5-1}=2,7^4=53,1441$

f) $\left(5^3\right)^7=5^{3\cdot \:7}=5^{21}=476837158203125$

3.

a) 1

b) -1

c) 1

d) -1

4.

a) $2^{-1}=\frac{1}{2}$

b) $-2^{-4}=-\frac{1}{2^4}=-\frac{1}{16}$

c) $-\left(-4\right)^{-3}=-\frac{1}{\left(-4\right)^3}=-\frac{1}{-64}=\frac{1}{64}$

d) $\left(-2\right)^{-2}=\frac{1}{\left(-2\right)^2}=\frac{1}{4}$

e) $-\left(-7\right)^2=-7^2=-49$

f) $\left(\frac{1}{2}\right)^{-1}=\frac{1}{\frac{1}{2}}=2$

g) $\left(-\frac{1}{3}\right)^{-2}=\frac{1}{\left(-\frac{1}{3}\right)^2}=\frac{1}{\frac{1}{9}}=9$

h) $-\left(-\frac{1}{6}\right)^{-1}=-\frac{1}{-\frac{1}{6}}=6$

i) $-\left(-\frac{3}{2}\right)^{-3}=-\frac{1}{\left(-\frac{3}{2}\right)^3}=-\frac{1}{-\frac{27}{8}}=\frac{8}{27}$

j) $\left(-\frac{2}{5}\right)^{-2}=\frac{1}{\left(-\frac{2}{5}\right)^2}=\frac{1}{\frac{4}{25}}=\frac{25}{4}$

5.

a) $100000000=10^8$

b) $0,00001 =10^{-5}$

c) $0,0000001=10^{-7}$

d) $1000=10^3$