Question

Teoría de exponentes

Answer 1

Respuesta:

1. N = 287

2. Sₓ = x⁵

4. M = 3

5. S = 4

Explicación paso a paso:

1.

Cambiar de forma a los exponentes:

(1 / 2)⁻¹ = (2⁻¹)⁻¹ = 2¹ = 2

(1 / 3)⁻¹ = (3⁻¹)⁻¹ = 3¹ = 3

(1 / 4)⁻¹ = (4⁻¹)⁻¹ = 4¹ = 4

Reemplazar:

N = (1 / 2)⁻² + (1 / 3)⁻³ + (1 / 4)⁻⁴

Luego:

(1 / 2)⁻² = (2⁻¹)⁻² = 2² = 4

(1 / 3)⁻³ = (3⁻¹)⁻³ = 3³ = 27

(1 / 4)⁻⁴ = (4⁻¹)⁻⁴ = 4⁴ = 256

Reemplazar:

N = 4 + 27 + 256

N = 287

2.

Multiplicar exponentes:

(x²)² = x⁴

(x³)² = x⁶

(x²)⁴ = x⁸

(x⁵)² = x¹⁰

(x³)³ = x⁹

Reemplazar:

Sₓ = [(x²)(x⁴)(x⁶)(x⁸)(x¹⁰)] / [x(x³)(x⁵)(x⁷)(x⁹)]

Al sumar exponentes:

Sₓ = [x³⁰] / [x²⁵]

Al restar exponentes:

Sₓ = x⁵

4.

Al factorizar :

M = [2ⁿ × 7²ⁿ (2³ × 7 - 2)] / [2ⁿ × 7²ⁿ(2⁵ - 2 × 7)]

Al simplificar:

M =  (2³ × 7 - 2) / (2⁵ - 2 × 7)

Luego:

M =  (8 × 7 - 2) / (32 - 2 × 7)

M =  (56 - 2) / (32 - 14)

M =  54 / 18

M = 3

5.

Cambiar de forma a los exponentes:  

√2 = 2¹/²

⁴√2 = 2¹/⁴

Reemplazar:

S = [√(2√(2¹(2¹/²))) / √(2(2¹/⁴))]⁸

Al sumar exponentes:

S = [√(2√(2³/²)) / √(2⁵/⁴)]⁸

S = [√(2¹(2³/²)¹/²) / √(2⁵/⁴)]⁸

Al multiplicar exponentes:

S = [√(2¹(2³/⁴)) / √(2⁵/⁴)]⁸

Al sumar exponentes:

S = [√(2⁷/⁴) / √(2⁵/⁴)]⁸

S = [√(2⁷/⁴ / 2⁵/⁴)]⁸

Al restar exponentes:

S = [√(2²/⁴)]⁸

S = [(2²/⁴)¹/²]⁸

Al multiplicar exponentes:

S = [2]²

S = 4