Corrigés 4AS Calcul numérique - Puissances

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A =

3 5

7

150 10 8 10 6 10

× × ×

×

A =

8 7

150 8 10 6 10

× ×

× ×× ×

× ×

×

A 6 25 8 10 6

× × ×

×× × ×× ×

× × ×

=

A====25 8 10× ×× ×× ×× ×

A====2000

A= ×= ×= ×= ×2 103

B=

5 2

7

2 10 1, 2 10 3 10

−

× × ×

××

B

5 2

7

2 1,2 10 10

= 3 10

−−

−

× ×

×

××

×

B 2, 4 ^{5 2 7}

3 10

− + +

− + +− + +

− + +

= ×

B= 0,8 10×××× ⁴ B= ×= ×= ×= ×8 103

3 10

2

49 10 6 10

C 14 10

−

× × ×

===

= ××××

7 2

7 7 3 2 10

C 7 2 10

−

−−

−

−−

× × × ×

× × × ×× × × ×

× × × ×

=

= × ×× ×× ×× ×

-7-(-2)

C=7 3 10× ×× ×× ×× ×

Corrigés 4AS Calcul numérique - Puissances

1

2

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www.maurimath.net 2 Horma Hamoud C====21 10×××× ^{− − −}^{− − −}^{− − −}^{− − −}^{7 ( 2)}

-5 5

C=21 10 21

× =10

× =

C 21

100000

==

B = 7 ×××× (7^{– 2})^{– 4} 7¹¹

B = 7 ×××× 7⁸ 7¹¹

B = 7^{1 + 8} 7¹¹

B = 7⁹ 7¹¹

11 9

B 1 7 ⁻⁻⁻⁻

==

2

B 1

=7

==

=

B 1

=49

==

=

8

8 10 10 10 8 10 8 2

8

1 1

X=( ) 3 = 3 1 3 3 3 =3

3 3

− −

× × = × × =

5 5 6

5 6 5 6 6 5 -1 1

5 6

4 3 ( 1) 4 3 3

Y=(- ) ( ) 4 3 =-4 3

3 4 3 4 4

− −

−− −−

− −

− ×

× = × = − × × = −

×× == ×× = −= − ×× ×× = −= −

× = × = − × × = −

2011 2 2011 3 2011 2 2011 3 2 2011 2011

Z (1, 5) ( ) ( ) ( ) ( ) =1 1

3 2 3 2 3

= × = × = × =

== ×× == ×× == ×× ==

= × = × = × =

1) On a (2 )^{3 5} ====2^{3 5}^×^×^×^× ====2¹⁵ , et 2³⁵ ====2^{3 3 3 3 3}^{× × × ×}^{× × × ×}^{× × × ×}^{× × × ×} ====2²⁴³^. Or 234>>>>15^{, donc}

35 3 5

2 >>>>(2 ) ^. 4

3

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www.maurimath.net 3 Horma Hamoud 2) A= −= −= −= −( 3)²+ ×+ ×+ ×+ ×5 2² ====9 5 4+ ×+ ×+ ×+ × , (Le calcul de puissance est prioritaire…)

A ====9++++20 (La multiplication est prioritaire sur l’addition).

A====29

2 5

B= × −= × −= × −= × −2 ( 4) + × −+ × −+ × −+ × −6 ( 1) = ×= ×= ×= ×2 16 6 ( 1)+ × −+ × −+ × −+ × − ====32 6−−−− ====26^.

2 3 5

A= −= −= −= −( a b )⁻⁻⁻⁻ ⁻⁻⁻⁻ ⁼

10

5 2 5 3 5 10 15

15

( 1) (a ) (b ) a b a

b

− − − − −

− − − − − −−−−

− = − × =

a ² 5 ² B ( ) ( )

5 b

−

= × −

= ×

2 2 2

2

2 2 2

a b a b

5 ( )5 5 5

= × = ×

== ×× == ××

= × = ×

2 2 4

a b

= 5

=

==

2 3 2 2

C ( 2a b ) 4a b

−

= −

==

=

2 3 2 2

( 2a b ) 4a b

−

−−

× −

×

× ⁼

2 2

6 6

2 2 2

2a b 2a b

( ) ( )

4a b 2 2a b b

− −

=

==

= ×××× ××××

6 6 6

( 1 ) 2 b 2b

−

= − = ×

= = ×

= = × ^.

5 2 2 5 2 2 ( 2) 10 ( 4) 10 6 16

16 13

1 3 3 ( 1) 3 3 3 2 3 9 9 4 13

(3 2 ) 3 2 3 2 3 3 3

A 3 2

(9 2 ) 9 2 (3 ) 2 2 2 2

− × × − −

−

− − × × −

× × × ×

= = = = = = ×

× × × ×

×× ×× ×× ××

× × × ×

3 3 2 2 6 6 8 6 2

8 2 2 2 2 4 4 2 2

2 5 10 2 2 5 5 2 5

B 4 25 5 (2 5 ) 2 (2 5) 2 5 2 2 5

− −

−− −−

− −

 

 ××××  ×××× ×××× ××××

= ÷ = × =

=  ÷ = × =

× × × × × × × ×

 

6 2 6 2

1 4

4 4 2 2 7 6

2 5 2 5

2 5 2 5 2 2 5 2 5

− −

−− −−

− −

× ×

= = = ×

× × × × ×

×× × ×× × ×× ××

× × × × ×

3

71 48 119 71 48 119 2 71 71 48 119

2

125 5

C 40 (1, 25) 10 (4 10) ( ) 10 (2 ) 10 ( ) 10

100 10

− − −

= × × = × × × = × × ×

144

142 71 119 142 71 96 144 119 142 142 2 215 71

96

2 10 5 10 2 10 10 5 10 2 5 5 10 10

10

− − − −

= × × × = × × × × = × × × ×

142 142 2 144 142 144 2

2 5⁻⁻⁻⁻ 5 10⁻⁻⁻⁻ 10 10⁻⁻⁻⁻ 5

= × × × = × ×

² ² ² ² ² ² 1

10 5 2 5 5 2

4

− − − −

= × = × × = =

6 5

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100 50 149 100 3 50 149 2 100 100 50 50 149 149

D 12 (1, 5) 6 (4 3) ( ) (2 3) (2 ) 3 3 2 2 3

2

− − − − −

= × × = × × × × = × × × × ×

== ×× ×× == ×× ×× ×× ×× == ×× ×× ×× ×× ××

= × × = × × × × = × × × × ×

====2²⁰⁰× ×× ×× ×× ×3 2⁻⁻⁻⁻¹⁹⁹ = × == × == × == × =2 3 6

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