Question

Determine o valor de x em cada caso

Answer 1

512/2
256/2
128/2
64/2
32/2
16/2
8/2
4/2
2/2
1

(2×2×2)×(2×2×2)×(2×2×2)
___2_____2_____2

2×2×2= 8

$\sqrt[3]{512} = 8$

343/7
49/7
7/7
1

(7×7×7)
__7

$\sqrt[3]{343} = 7$

c)

121/11
11/11
1

$\sqrt[4]{11}^{2} \times \sqrt[4]{11} ^{2} = {11}^{ \frac{2}{4} } \times {11}^{ \frac{2}{4} } \\ {11}^{ \frac{2}{4} + \frac{2}{4} } \\ {11}^{ \frac{4}{4} } = {11}^{1} = 11$

d)

$\sqrt{ \frac{2744}{14} } = \sqrt{196} = 14$

e)

3,2×10^6= 32×10^5

32/2
16/2
8/2
4/2
2/2
1

2^5

$\sqrt[5]{32} \times \sqrt[5]{ {10}^{5} } \\ \sqrt[5]{ {2}^{5} } \times \sqrt[5]{ {10}^{5} } \\ 2 \times 10 = 20$

f)

5)

a)

$\sqrt[12]{ {2}^{8} } = \sqrt[3]{ {2}^{2} }$

b)

$\sqrt[10]{ {3}^{15} } = \sqrt[2]{ {3}^{3} }$

c)

$\sqrt[27]{512} = \sqrt[27]{ {2}^{9} } = \sqrt[3]{ {2}^{1} }$

d)

$\sqrt[10]{ \frac{81}{625} } = \sqrt[10]{ \frac{ {3}^{4} }{ {5}^{4} } } = \\ \sqrt[5]{ \frac{ {3}^{2} }{ {5}^{2} } }$

e)

125/5
25/5
5/5
1

5^3

729/9
81/9
9/9
1

9^3

$\sqrt[ \times ]{ \frac{5}{9} } = \sqrt[6]{ \frac{125}{729} } = \sqrt[6]{ \frac{ {5}^{3} }{ {9}^{3} } } \\ \sqrt[2]{ \frac{ {5}^{1} }{ {9}^{1} } }$

f)

2401/7
343/7
49/7
7/7
1

7^4

625/5
125/5
25/5
5/5
1

5^4

$\sqrt[8]{ \frac{2401}{625} } = \sqrt[8]{ \frac{ {7}^{4} }{ {5}^{4} } } \\ \sqrt[2]{ \frac{7}{5} }$