Question

Calculați :
a)10^60:(2x5)^58
b)(7^14x5)^2:7^26
c)(7^6)^8:49^24
d)(3^4)^9:(9^6)^3
e)(11^2011x4^1005):[(22^2)^5]^201
f)2^23:2^21:2+3^32:3^31x3

Answer 1

a)   10⁶⁰ : ( 2 x 5 )⁵⁸ = 10⁶⁰ : 10⁵⁸ = 10 ⁽ ⁶⁰ ⁻ ⁵⁸ ⁾ = 10² = 100

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b)  ( 7¹⁴ x 5 ) ² : 7²⁶ = 7²⁸ x 5² : 7²⁶ = 7² x 5² = ( 7 x 5 )² = 35² = 1 225

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

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d)  ( 3⁴ )⁹ : ( 9⁶ )³ = 3³⁶ : ( 3² ) ¹⁸ = 3 ⁽ ³⁶ ⁻ ³⁶ ⁾ = 3⁰ = 1

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

= ( 11²⁰¹¹ x 4¹⁰⁰⁵ ) : [ ( 2² x 11² )⁵ ] ²⁰¹ =

= ( 11²⁰¹¹ x 4¹⁰⁰⁵ ) : ( 11²⁰¹⁰ x 4¹⁰⁰⁵ ) =

= 11

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

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

= 2¹ + 3⁰ =

= 2 + 1 =

= 3