`2^4*5^4 = ?`

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

`12^3:3^3 = ?`

`= (12/3)^3 `
`= 4^3 `
`= 64`

`15^2:5^2 = ?`

`= (15/5)^2`
`= 3^2`
`= 9`

`8^-2*2^-2 = ?`

`= (8*2)^-2`
`= 16^-2`
`= 1/(16^2)`
`= 1/256`

`2,5^3:5^3 = ?`

`= (2,5/5)^3 `
`= 0,5^3`
`= 0,125`
`= 1/8`

`(-18)^5 : 9^5 = ? `

`= -(18/9)^5`
`= -2^5`
`= -32`

`(-18)^4 : 9^4 = ? `

`= (18/9)^4`
`= 2^4`
`= 16`

`(1/5)^-2*(3/5)^-2 = ?`

`=5^2*(5/3)^2`
`= 25* 25/9`
`= 625/9`

`18^-3:6^-3 = ?`

`= (18/6)^-3`
`= 3^-3`
`= 1/27`

`3^a*6^a = ?`

`= (3*6)^a`
`= 18^a`

`(2/3)^n*6^n = ?`

`= (2/3 *6)^n`
`= 4^n`

`10^p:5^p = ?`

`= (10/5)^p`
`= 2^p`

`2,4^x:(-0,8)^x = ?`

`= (2,4/-0,8)^x`
`= (-3)^x`

`4,5^k:3^k = ?`

`= (4,5/3)^k`
`= 1,5^k`

`4^(2a)*3^(2a) = ?`

`= (4*3)^(2a)`
`= 12^(2a)`
`= (12^2)^a`
`= 144^a`

Welches Vorzeichen hat   `(-2)^k` ?

Wenn k gerade ist, hat   `(-2)^k`   positives Vorzeichen.
Wenn k ungerade ist, hat   `(-2)^k`   negatives Vorzeichen.

`15^-b:10^-b = ?`

`= (15/10)^-b`
`= (3/2)^-b`
`= (2/3)^b`

`5^(2n):5^(2n) = ?`

`= 1`
 
`a/a = 1`   für alle a,   also auch
`5^(2n)/(5^(2n)) = 1`

`8^(2-x):4^(2-x) = ?`

`= (8/4)^(2-x)`
`= 2^(2-x)`
`= 2^2:2^x`
`= 4/2^x`

`2^(n+1)*(1/2)^(n+1) = ?`

`= (2*1/2)^(n+1)`
`= 1^(n+1)`
`= 1`

`2^(n+1):(1/2)^(n+1) = ?`

`= (2:1/2)^(n+1)`
`= 4^(n+1)`
`= 4*4^n`

`(2x)^(k+1):x^(k+1)=?`

`= ((2x)/x)^(k+1)`
`= 2^(k+1)`
`= 2*2^k`

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

`=(3/4*4/3)^12`
`=1^12`
`= 1`

`(1/2)^(2n)*(2/3)^(2n) = ?`

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

`(4/3)^4*(3/2)^4*(11/2)^4 = ?`

`=(4/3 * 3/2 * 11/2)^4`
`= 11^4`

`8*4^3 = ?`     Schreibe anders, rechne nicht aus.

`=2*4*4^3`
`=2*4^4`

`32*x^5 = ?`

`= 2^5*x^5`
`= (2x)^5`

`(a^2*b^3)^n = ?`     Schreibe ohne Klammer.

`= a^(2n)*b^(3n)`

`(x^3*y^-4)^(2k) = ?`     Schreibe ohne Klammer.

`=x^(6k)*y^(-8k)`

`(u^-5*v^3)^(n+1) = ?`     Schreibe ohne Klammer.

`= u^(-5*(n+1))*v^(3*(n+1))`
`= u^(-5n-5)*v^(3n+3)`

`(a^(k-1)*b^k)^(k+1) = ?`     Schreibe ohne Klammer.

`= a^((k-1)*(k+1))*b^(k*(k+1))`
`= a^(k^2-1)*b^(k^2+k)`

`(r^x*q^y)^(x-y) = ?`     Schreibe ohne Klammer.

`=r^(x*(x-y))*q^(y*(x-y))`
`= r^(x^2-y)*q^(xy-y^2)`

`(2x)^3 = ?`

`=2^3*x^3`
`=8x^3`

`(6ab)^4 = ?`     Schreibe ohne Klammer.

`= 6^4*a^4*b^4`

`(xy)^-2 = ?`

`= 1/(xy)^2 `
`= 1/(x^2y^2)`

`6^5*3^-5 = ?`

`=6^5/3^5`
`= (6/3)^5`
`= 2^5 `
`= 32`

`5^-3:10^3 = ?`

`=1/(5^3*10^3)`
`= 1/(50^3)`
`= 1/(125::000)`

`(25^0)^3 = ? `

`= 1^3`
`= 1`

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

`= (3/2)^2*(3/2)^2`
`= (3/2)^4`
`= (3^4)/(2^4)`
`= 81/16`

`5^-x*10^x = ?`

`= (10^x)/(5^x)`
`= (10/5)^x`
`= 2^x`

`(2/5)^-k:(4/5)^k = ?`

`=(5/2)^k*(5/4)^k`
`= (5/2 * 5/4)^k`
`= (25/8)^k`