Question

utilizando o raciocínio acima, descubra o valor de cada expressão:

a) 2³ . 4² . 8¯² =

b) 3² . 27¯¹ . 9¹ =

c) 5³ . 25¯¹ . 625° =

d) 4³ . 27¯² . 32¯¹ . 2¹ . 9³ =

e) 10³ . 25¯² . 20¯² . 2² . 5³ =

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Answer 1

Resposta:

a)

2³ × (2²)² × (2³)⁻²=

2³ × 2⁴ × 2⁻⁶ =

2³⁺⁴⁻⁶ = 2⁷⁻⁶ = 2¹ = 2

-----------------------------------

b)

3² × ( 3³)⁻¹ ×(3²)¹=

3² × 3⁻³ × 3² =

3²⁻³⁺² = 2⁴⁻³ = 2¹ = 2

-------------------------------------

c)

5³ × ( 5²)⁻¹ × ( 5⁴)⁰ =

5³ × 5⁻² × 5⁰ =

5³⁻²⁺⁰ = 5¹ = 5

---------------------------

d)

(2²)³ × (3³)⁻² × (2⁵)⁻¹ × (3²)³=

2⁶ × 3⁻⁶ × 2⁻⁶ × 3⁶ =

2⁶ × 2⁻⁶ × 3⁻⁶ × 3⁶ =

2⁶⁻⁶ × 3⁻⁶⁺⁶ =

2⁰ × 3⁰ = 1 × 1 = 1

-------------------------------

e)

(2 × 5 )³ × (5²)⁻² × ( 2² × 5 )⁻² ×2² × 5³=

2³ × 5³ × 5⁻⁴ × 2⁻⁴ × 5⁻² × 2² × 5³=

2³ × 2⁻⁴ × 2² × 5³ × 5⁻⁴ × 5⁻² × 5³=

2³⁻⁴⁺² × 5³⁻⁴⁻²⁺³ =

2⁵⁻⁴ × 5⁶⁻⁶ =

2¹ × 5⁰ = 2 × 1 = 2

Answer 2

Explicação passo-a-passo:

a) 2³ . 4² . 8¯² =

2³. (2.2)². (2.2.2)¯²

2³. (2²)². (2³)⁻²

2³. 2⁴. 2⁻⁶

2³⁺⁴⁻⁶

2¹

= 2

b) 3² . 27¯¹ . 9¹ =

3². (3.3.3)⁻¹. (3.3)¹

3². (3³)⁻¹. (3²)¹

3². 3⁻³. 3²

3²⁻³⁺²

3¹

= 3

c) 5³ . 25¯¹ . 625⁰ =

5³. (5.5)⁻¹. (5.5.5.5)⁰

5³. (5²)⁻¹. (5⁴)⁰

5³. 5⁻². 1

5³⁻². 1

5¹. 1

= 5

d) 4³ . 27¯² . 32¯¹ . 2¹ . 9³ =

(2.2)³. (3.3.3)². (2.2.2.2.2)⁻¹. 2¹. (3.3)³

(2²)³. (3³)². (2⁵)⁻¹. 2¹. (3²)³

2⁶. 3⁶. 2⁻⁵. 2¹. 3⁶

2⁶⁻⁵⁺¹. 3⁶⁺⁶

2². 3¹⁸

= 2.125.764

e) 10³ . 25¯² . 20¯² . 2² . 5³ =

(2.5)³. (5.5)⁻². (2.2.5)⁻². 2². 5³

(2.5)³. (5²)⁻². (2².5)⁻². 2². 5³

2³. 5³. 5⁻⁴. 2⁻⁴. 5⁻². 2². 5³

2³⁻⁴⁺². 5³⁻⁴⁻²⁺³

2¹. 5⁰

= 2