Question

01. Calcule:

a)64½=

b)8⅔=

c)16½

d)27⅓

e)(²⁵)½
⁸¹​

Answer 1

Resposta:

Olá!

Explicação passo-a-passo:

1. a) $64^{1/2}=\sqrt{64}=\sqrt{2^6} =\sqrt{2^2.2^2.2^2}= 2.2.2=8$

b) $8^{2/3}=\sqrt[3]{8^2}=\sqrt[3]{64}=\sqrt[3]{4^3}=4$

c) $16^{1/2}=\sqrt{16}=\sqrt{2^4}=\sqrt{2^2.2^4}=2.2=4$

d) $27^{1/3}=\sqrt[3]{27}=\sqrt[3]{3^3}=3$

e) $(\frac{25}{81})^{1/2}=\sqrt{\frac{25}{81} }=\sqrt{\frac{5^2}{9^2} }=\frac{5}{9}$

Outra forma de calcular:

a) $64^{1/2}=(2^6)^{1/2}=2^{6/2}=2^3=2.2.2=8$

b) $8^{2/3}=(2^3)^{2/3}=2^{6/3}=2^2=2.2=4$

c) $16^{1/2}=(2^4)^{1/2}=2^{4/2}=2^2=2.2=4$

d) $27^{1/3}=(3^3)^{1/3}=3^{3/3}=3^1=3$

e) $(\frac{25}{81})^{1/2}=\frac{25^{1/2}}{81^{1/2}}=\frac{(5^2)^{1/2}}{(9^2)^{1/2}}=\frac{5^{2/2}}{9^{2/2}}=\frac{5^1}{9^1}=\frac{5}{9}$

Bons Estudos!