Question

calcula el valor de cada expresión usando las propiedades de la potenciación correspondientes

Answer 1

El enunciado completo es el siguiente:

calcula el valor de cada expresión usando las propiedades de la potenciación correspondientes:

• (7/9)³

• (- 7/3)⁴

• (3/6)²

• (2/6)(2/6)⁰(2/6)²(2/6)³

• (- 3/9) (- 3/9)⁻¹

• [(- 7/5)²]³

• [(3/7)³]²

• [(1/3)²]³ (1/3)²

• [(5/7)²]² (5/7)²

• (4/3)⁴ ÷ (4/3)²

Resolviendo cada una, nos queda:

• (7/9)³

(7³/9³)

(343/729)

• (- 7/3)⁴

(-7⁴/3⁴)

(- 2.401/81)

• (3/6)²

(3²/6²)

(9/36)

(1/4)

• (2/6)(2/6)⁰(2/6)²(2/6)³

(2/6)⁽¹ ⁺ ⁰ ⁺ ² ⁺ ³⁾

(2/6)⁶ = (1/729)

• (- 3/9) (- 3/9)⁻¹

(- 3/9)/(- 3/9)

1

• [(- 7/5)²]³

(- 7/5)⁽² ˣ ³⁾

(- 7/5)⁶ = (- 117.649/15.625)

• [(3/7)³]²

(3/7)⁽³ ˣ ²⁾

(3/7)⁶ = (729/117.649)

• [(1/3)²]³ (1/3)²

(1/3)⁽² ˣ ³⁾ (1/3)²

(1/3)⁶(1/3)²

(1/3)⁽⁶ ⁺ ²⁾

(1/3)⁸

• [(5/7)²]² (5/7)²

(5/7)⁽² ˣ ²⁾ (5/7)²

(5/7)⁴ (5/7)²

(5/7)⁽⁴ ⁺ ²⁾

(5/7)⁶

• (4/3)⁴ ÷ (4/3)²

(4/3)⁽⁴ ⁻ ²⁾

(4/3)²

Answer 2

Respuesta:

a) (7/9)^3 = 343/729

b) (-7/3)^4=2401/81

c) (-6/2)^5= -243

d)  (3/6)^2= 1/4

e) (2/6)*(2/6)^0*(2/6)^2*(2/6)^3=1/729

f) (-3/9)*(-3/9)^-1 =1

g) [(-7/5)^2]^3 = 7^6/5^6 = 117649/15625

h) [(3/7)^3]^2= 3^6/7^6= 729/117649

i) [(1/3)^2]^3*(1/3)^2 = (1/3)^8

j) [(5/7)^2]^2 * (5/7)^2 =  (5/7)^6

k) (3/8)^7÷(3/8)^2=(3/8)^5    

l) ( 4/3)^4÷(4/3)^2=  (4/3)^2 = 4^2/3^2=16/9

m) [(-2/4)^4*(5/3)^-4]/[(-2/4)*(3/5)] = 81/10000

n) [(-3/4)^3 ÷ (-3/4)^5]^4=( 4/3)^8

a. ( 7/9)^3= 7^3/9^3= 343/729

b. (-7/3) elevado a la cuarta:

     (-7/3)⁴ =  7⁴/3⁴ = 2401/81

c. (-6/2) elevado a la quinta :

    (-6/2)^5 = (-3)^5 = -243

d.  (3/6) elevado al cuadrado  :

      (3/6)² = (1/2)² = 1/4

Explicación:

 Dos sextos por dos sextos elevado a cero por dos sextos elevado al cuadrado por dos sextos elevado al cubo :

   ( 2/6)* (2/6)⁰* (2/6)² *(2/6)³ = ( 2/6)⁶ = ( 1/3 )⁶ = 1⁶ /3⁶ = 1/729

f. Menos tres novenos por menos tres novenos elevado menos uno:

     (-3/9) * (-3/9)⁻¹  = ( -1/3)* ( - 9/3)¹ = (-1/3)*(-3)¹ = 1

g. [(-7/5)^2]^3 = ( -7/5)^6= 7^6/5^6 = 117649/15625

h. [(3/7)^3]^2=(3/7)^6= 3^6/7^6= 729/117649

i. [(1/3)^2]^3*(1/3)^2 =(1/3)^6*(1/3)^2= (1/3)^8

j.  [(5/7)²]² por (5/7) elevado al cuadrado :

    (5/7)⁴* (5/7)² = (5/7)⁶  = 5⁶/7⁶ = 15625/117649  

k.  (3/8) elevado a la séptima dividido (3/8) elevado al cuadrado :

        (3/8)⁷  ÷ (3/8)² = ( 3/8 )⁵  

l. ( 4/3)^4÷(4/3)^2=16/9

m. [(-2/4)^4*(5/3)^-4]/[(-2/4)*(3/5)] =

    = (-2/4)^4*(3/5)^4 = (-1/2)^4*(3/5)^4= 1/16*81/625

    =  81/10000

n . [(-3/4)³ ÷ (-3/4)⁵]⁴  = [ ( -3/4)⁻²]⁴ = [ ( - 4/3)²]⁴ = ( - 4/3)⁸ = (4/3)⁸