Question

ASSUNTO: POTÊNCIAS E SUAS PROPRIEDADES

Answer 1

Oie, Td Bom?!

1.

a)

5⁰ = 1

b)

2⁵ = 2 . 2 . 2 . 2 . 2 = 32

c)

(- 2)³ = - 2³ = - (2 . 2 . 2) = - 8

d)

(- 7)¹ = - 7

e)

(- 6)² = 6² = 6 . 6 = 36

f)

(3/2)⁴ = 3⁴/2⁴ = 81/16 = 5,0625

2.

a)

3⁵ . 3² . 3⁴ = 3⁵⁺²⁺⁴ = 3¹¹

b)

5⁷ . 5⁻² = 5⁷⁺⁽⁻²⁾ = 7⁷⁻² = 7⁵

c)

15⁷ ÷ 15² = 15⁷⁻² = 15⁵

d)

12⁻⁵ ÷ 12³ = 12⁻⁵⁻³ = 12⁻⁸

e)

(7¹⁰)² = 7¹⁰ˣ² = 7²⁰

f)

(- 3⁻⁵)² = (3⁻⁵)² = 3⁻⁵ˣ² = 3⁻¹⁰

3.

a)

6⁻² = 1/6² = 1/36 ≈ 0,02777...

b)

5⁻³ = 1/5³ = 1/125 = 0,008

c)

(2/5)⁻³ = (5/2)³ = 5³/2³ = 125/8 = 15,625

d)

(- 5)⁻² = 5⁻² = 1/5² = 1/25 = 0,04

4.

a)

5^{¾} = ∜[5³] = ∜[125]

b)

(3/4)^{⅔} = ∛[(3/4)²] = ∛[9/16]

c)

(1/25)^{⅖} = ⁵√[(1/25)²] = ⁵√[1/625]

5.

a)

= 6³ . 6² ÷ (6⁻² . 6⁵)

= 6³ . 6² ÷ (6⁻²⁺⁵)

= 6³ . 6² ÷ 6³

= 1 . 6²

= 6²

= 6 . 6

= 36

Att. Makaveli1996

Answer 2

Explicação:

$1)a) 5^{0} = 1$

$b)$

$2^{5} = \\2 . 2 . 2 . 2 . 2 \\4. 2 . 2 . 2 \\8. 2 . 2\\16 . 2 \\32$

$c)$

$(-2)^{3} =\\-2 . -2 . -2\\+4. -2\\-8$

$d)$

$(-7)^{1} = -7$

$e)$

$(-6)^{2} = \\(-6) . (-6)\\+36$

$f)$

$(3/2)$⁴ $= 3$⁴$/2$⁴$= 81/16 = 5,0625$

$2a)$

$3$⁵ $. 3$² $. 3$⁴ $=$

=> Conserva a base e soma os expoentes.

$3$¹¹

$b)$

$5$⁷ $. 5$⁻² $= 5$⁵

$c)$

$15$⁷ ÷ $15$² $= 15$⁵

$d)$

$12$⁻⁵ ÷ $12$³ $= 12$⁻⁸

$e)$

$(7$¹⁰$)$²$= 7$²⁰

$f)$

$(- 3$⁻⁵$)$² $= 3$⁻¹⁰

$3)a)$

$6$⁻² $=$ $\frac{1}{36}$ ≅ $0,02777...$

$b)$

$5$⁻³ $=$ $\frac{1}{5^{3} } = \frac{1}{125} =0,008$

$c)$

$(2/5)$⁻³ $= (5/2)$³ $= 5$³$/2$³ $= 125/8 = 15,625$

$d)$

$(- 5)$⁻² $= 5$⁻² = $\frac{1}{5} ^{2}$ $= \frac{1}{25} = 0,04$          

$4)a)$

5^{¾} = ∜[5³] = ∜[125]

$b)$

(3/4)^{⅔} = ∛[(3/4)²] = ∛[9/16]

$c)$

(1/25)^{⅖} = ⁵√[(1/25)²] = ⁵√[1/625]

$4)a)$

6³ . 6² ÷ (6⁻² . 6⁵)

6³ . 6² ÷ (6⁻²⁺⁵)

6³ . 6² ÷ 6³

1 . 6²

6²

6 . 6

36