Question

1) Calcule:

A) RAIZ QUARADA 169=
B) ³ RAIZ QUADRADA DE 512 =
C) 4 ELEVADO RAIZ QUADRADA DE 1 SOBRE 16 =
D) RAIZ QUADRADA DE 0,25
E) 8 ELEVADO A 2 SOBRE 3

F) 144 ELEVADO A -1 SOBRE 2
G) 16 ELEVADO A 5 SOBRE 2

H) 27 ELEVADO A 2 SOBRE 3

I) 4 √256 . √25 - 16

J) 3 ELEVADO√1+ √49

Answer 1

Lembrando:

$\sqrt[m]{a^{n}}\rightleftharpoons a^{\frac{n}{m}}\\(a^{x})y\rightleftharpoons a^{x\cdot y}\\\\\\x^{-a}=\dfrac{1}{x^{a}}$
________________________

a)

$\sqrt{169}=\sqrt[2]{13^{2}}\\\sqrt{169}=13^{\frac{2}{2}}\\\sqrt{169}=13^{1}\\\sqrt{169}=13$

b)

$\sqrt[3]{512}=\sqrt[3]{2^{9}}\\\sqrt[3]{512}=2^{\frac{9}{3}}\\\sqrt[3]{512}=2^{3}\\\sqrt[3]{512}=8$

c)

$4^{\sqrt{1/16}}=4^{\sqrt{1}/\sqrt{16}}\\4^{\sqrt{1/16}}=4^{1/4}\\4^{\sqrt{1/16}}=(2^{2})^{1/4}\\4^{\sqrt{1/16}}=2^{2\cdot1/4}\\4^{\sqrt{1/16}}=2^{1/2}\\4^{\sqrt{1/16}}=\sqrt[2]{2^{1}}\\4^{\sqrt{1/16}}=\sqrt{2}$

d)

$\sqrt{0,25}=\sqrt{\dfrac{1}{4}}\\\\\\\sqrt{0,25}=\dfrac{\sqrt{1}}{\sqrt{4}}\\\\\\\sqrt{0,25}=\dfrac{1}{2}\\\\\\\sqrt{0,25}=0,5$

e)

$8^{2/3}=(2^{3})^{2/3}\\8^{2/3}=2^{3\cdot2/3}\\8^{2/3}=2^{2}\\8^{2/3}=4$

f)

$144^{-1/2}=\dfrac{1}{144^{1/2}}\\\\\\144^{-1/2}=\dfrac{1}{(12^{2})^{1/2}}\\\\\\144^{-1/2}=\dfrac{1}{12^{1}}\\\\\\144^{-1/2}=\dfrac{1}{12}$

g)

$16^{5/2}=(2^{4})^{5/2}\\16^{5/2}=2^{4\cdot5/2}\\16^{5/2}=2^{2\cdot5}\\16^{5/2}=2^{10}\\16^{5/2}=1024$

h)

$27^{2/3}=(3^{3})^{2/3}\\27^{2/3}=3^{3\cdot2/3}\\27^{2/3}=3^{2}\\27^{2/3}=9$

i)

$4\sqrt{256}\cdot\sqrt{25}-16=4\sqrt[2]{16^{2}}\cdot\sqrt[2]{5^{2}}-16\\4\sqrt{256}\cdot\sqrt{25}-16=4\cdot16\cdot5-16\\4\sqrt{256}\cdot\sqrt{25}-16=16\cdot(4\cdot5-1)\\4\sqrt{256}\cdot\sqrt{25}-16=16\cdot(20-1)\\4\sqrt{256}\cdot\sqrt{25}-16=16\cdot19\\4\sqrt{256}\cdot\sqrt{25}-16=304$

j)

$3^{\sqrt{1}+\sqrt{49}}=3^{1+7}\\3^{\sqrt{1}+\sqrt{49}}=3^{8}$

Answer 2

Resposta:

olá

Explicação passo-a-passo:

acho que tem erros na outra resposta que fizeram para te ajudar porque eu fiz e ...... mas ok

bons estudos!!