`2^3 = ?`

`8`

`4^-3 = ?`

`= 1/4^3`
` = 1/64`

`(-7)^2 = ?`

`= (-7)*(-7)`
`= 49`
 

`(-2)^5 = ?`

`=(-2)*(-2)*(-2)*(-2)*(-2)`
`=-2^5`
`=-32`
 

`(-5)^4 = ?`

`= (-5)*(-5)*(-5)*(-5)`
`= 5^4`
`= 625`

`(1/2)^3 = ?`

`= (1/2)*(1/2)*(1/2)`
`= 1/2^3)`
`= 1/8`

`(2/3)^-2 = ?`

`= (3/2)^2`
`= (3^2)/(2^2)`
`= 9/4`

`-3^2 = ?
 
Was hat Vorrang:
Vorzeichen oder Potenzierung?

Potenzierung hat Vorrang.
 
Man muss zuerst `2^3` rechnen und
dann erst ein Minus davor machen.
 
`-3^2 = -(3^2) = -9`
 

`-4^2 = 16`
 
Richtig?

Falsch.
 
`-4^2 = -(4^2) = -16`
 
Potenzierung hat Vorrang vor Vorzeichen.

`5^6*5^-7 = ?`

`= 5^(6-7) `
`= 5^-1 `
`= 1/5`
`= 0,2`
 

`3^-6*3^-7 = ?`

`= 3^(-6-7) `
`= 3^-13 `
`= 1/3^13`
 

`0,5^-4*0,5^5 = ?`

`= 0,5^(-4+5)`
`= 0,5^1`
`= 0,5`
 

`(1/2)^-2*(1/2)^-1 = ?`

`= 2^2*2^1`
`= 2^3`
`= 8`
 

`(3/4)^-5*(3/4)^4 = ?`

`= (3/4)^(-5+4)`
`= (3/4)^-1`
`= 4/3`
 

`7^3*7^0 = ?`

`=7^3*1 `
`=7^3 `
 

`3*2^4*5^4 = ?`

`=3*(2*5)^4 `
`=3*10^4 `
`=30::000 `
 

`6^-2*5*2^-2 = ?`

`= 5/(6^2*2^2)`
`= 5/144`
 

`3^-2*4*(1/2) = ?`

`=4/(9*2) `
`=2/9 `
 

`(3*4^3)/12^3 = ?`

`= (3*4^3)/(3*4)^3`
`= (3*4^3)/(3^3*4^3)`
`= 1/9`
 

`-2^2 = ?`

`=-4 `
 

`(-2)^2 = ?`

`= 4`
 

`(-2^2) = ?`

`= -4`
 

`-(2^2) = ?`

`= -4`
 

`2^-5 = ?`

`=1/2^5 `
`=1/32 `
 

`5^-2 = ?`

`=1/5^2 `
`=1/25 `
 

`(-2)^5 = ?`

`= -2^5`
`= -32`
 

`(-5)^-2 = ?`

`= 1/(-5)^2`
`= 1/5^2`
`= 1/25`
 

`-(5)^-2 = ?`

`= -1/5^2`
`= -1/25`
 

`(2^2)^4 = ?`

`=2^8 `
`=256 `
 

`(4^-3)^2 = ?`

`= 4^-6`
`= 1/4^6`
 

`(3^-2)^-3 = ?`

`=3^(2*3) `
`=3^6 `
 

`((-2)^3)^-2 = ?`

`= (-2)^-6`
`= 2^-6`
`= 1/2^6`
`= 1/64`
 

`((-0,5)^-2)^5 = ?`

`= ((-2)^2)^5`
`= (2^2)^5`
`= 2^10`
`=1024`

`(10^4)^-5 = ?`

`=10^-20 `
`=1/(10^20) `

Wie lauten die Vorrangregeln beim Rechnen?

1. Innere Klammer
2. Äußere Klammer
3. Potenzieren
4. Multiplizieren/Dividieren
5. Addieren/Subtrahieren

Berechne schrittweise nach den Vorrangregeln:
`[2+(3-4)*(5-2)^3]*2`

`=[2+(-1)*3^3]*2`     innere Klammern zuerst
`=[2+(-1)*27]*2`     Potenzieren
`=[2-27]*2`           Punkt vor Strich
`=[-25]*2`             Klammer
`=-50`