Question

ME AJUDEM NESSAS 5 QUESTÕES PFVV
1-De o valor das seguintes potências
a)22-⁴
b)10⁰
c)9⁸
Etc...
2-resolva conforme as propriedades e de o resultado:
a)
b)
c)
Etc...
3-...
4-...
5-....

Answer 1

Resposta:

01.

a) $\frac{1}{234256}$
b) $1$
c) $43046721$
d) $\frac{1}{100000}$
e) $85184$
f) $\frac{1}{970299}$
g) $\frac{1}{2}$

02.

a) $35721$
b) $\frac{1}{243}$
c) $400$
d) $0,00000009$
e) $9$
f) $16$
h) $48^8$

03.

a) Não
b) Sim
c) Não
d) Não
e) Sim
f) Não
g) Não

h) Sim

Explicação passo a passo:

01.

a) $22^{-4}=\frac{1}{22^4}=\frac{1}{234256}$
b) $10^0=1$
c) $9^8=43046721$
d) $10^{-5}=\frac{1}{10^5}=\frac{1}{100000}$
e) $44^3=85184$
f) $99^{-3}=\frac{1}{99^3}=\frac{1}{970299}$
g) $\left(\frac{1^3}{2}\right)=\frac{1}{2}$

02.

a) $9^3\cdot \:7^2=729\cdot \:7^2=729\cdot \:49=35721$
b) $3^{-3}\cdot \:3^{-2}=3^{-3-2}=3^{-5}=\frac{1}{3^5}=\frac{1}{243}$
c) $\left(5\cdot \:4\right)^2=20^2=400$
d) $\left(0,006\cdot \:0,5\cdot \:0,1\right)^2=0,006^2\cdot \:0,5^2\cdot \:0,1^2=0,000036\cdot \:0,5^2\cdot \:0,1^2=0,000036\cdot \:0,25\cdot \:0,1^2=0,000036\cdot \:0,25\cdot \:0,01=0,00000009$
e) $9^2\div \:3^2=81\div \:3^2=81\div \:9=9$
f) $4^3\div \:2^2=64\div \:2^2=64\div \:4=16$
h) $\left(48^2\right)^4=48^{2\cdot \:4}=48^8$

03.

a) $\sqrt{800}=\sqrt{2^5\cdot \:5^2}=\sqrt{2^4\cdot \:2\cdot \:5^2}=\sqrt{2^4}\sqrt{2}\sqrt{5^2}=4\sqrt{2}\sqrt{5^2}=4\sqrt{2}\cdot \:5=20\sqrt{2}$
b) $\sqrt{49}=\sqrt{7^2}=7$
c) $\sqrt{1342}$
d) $\sqrt{1000}=\sqrt{2^2\cdot \:2\cdot \:5^2\cdot \:5}=\sqrt{2^2}\sqrt{5^2}\sqrt{2\cdot \:5}=2\sqrt{5^2}\sqrt{2\cdot \:5}=2\cdot \:5\sqrt{2\cdot \:5}=10\sqrt{10}$
e) $\sqrt{400}=\sqrt{20^2}=20$
f) $\sqrt{1500}=\sqrt{2^2\cdot \:3\cdot \:5^3}=\sqrt{2^2\cdot \:3\cdot \:5^2\cdot \:5}=\sqrt{2^2}\sqrt{5^2}\sqrt{3\cdot \:5}=2\sqrt{5^2}\sqrt{3\cdot \:5}=2\cdot \:5\sqrt{3\cdot \:5}=10\sqrt{3\cdot \:5}=10\sqrt{15}$
g) $\sqrt{72}=\sqrt{2^3\cdot \:3^2}=\sqrt{2^2\cdot \:2\cdot \:3^2}=\sqrt{2^2}\sqrt{2}\sqrt{3^2}=2\sqrt{2}\sqrt{3^2}=2\sqrt{2}\cdot \:3=6\sqrt{2}$

h) $\sqrt{100}=\sqrt{10^2}=10$