Question

Calculați
b) (7^14×5)^2÷7^26
c) (7^6)^8÷49^24
d) (3^4)^9÷(9^6)3
e) (11^2011×4^1005)÷[(22^2)^5]^201
f) 2^23÷2^21÷2+3^32÷3^31×3

Answer 1

b)   ( 7¹⁴ x 5 )² : 7²⁶ = 7 ⁽ ¹⁴ ˣ ² ⁾  x 5² : 7²⁶ = 7²⁸ x 5² : 7²⁶ =

= 7² x 5² = ( 7 x 5 )² = 35²= 1 225

___________________________________

c) ( 7⁶ )⁸ : 49²⁴ = 7⁴⁸ : ( 7² ) ²⁴ = 7 ⁽ ⁴⁸ ⁻ ⁴⁸ ⁾ = 7⁰ = 1

_____________________________________

d)  ( 3⁴ )⁹ : ( 9⁶ )³ = 3³⁶ : ( 3² )¹⁸ = 3³⁶ : 3³⁶ = 1

___________________________________

e)   ( 11²⁰¹¹ x 4¹⁰⁰⁵ ) : [ ( 22² ) ⁵ ] ²⁰¹ = 11

= ( 11 ²⁰¹¹ x 2² ˣ ¹⁰⁰⁵ ) : 22 ² ˣ ⁵ˣ²⁰¹ =

= ( 11²⁰¹¹ x 2²⁰¹⁰ ) : 22²⁰¹⁰ =

= 11 x 22²⁰¹⁰ : 22 ²⁰¹⁰ =

= 11

_________________________

f)   2²³ : 2²¹ : 2 + 3³² : 3³¹ x 3 = 11

= 2 ⁽ ²³ ⁻ ²¹ ⁻ ¹ ⁾ + 3 ⁽ ³² ⁻ ³¹ ⁺ ¹ ⁾ =

= 2¹ + 3² =

= 2 + 9 =

= 11