a,

`(3*5)^2` = `15^2` = 225

vagy

`(3*5)^2` = `3^2*5^2` = `9*25` = 225


`(7*9)^0` = `63^0` = 1

`(7*9)^0` = `7^0*9^0` = `1*1` = 1


`(2*5)^3` = `10ˇ3` = 1000

`(2*5)^3` = `2^3*5^3` = `8*125` = 1000


b,

`0.2^4` = `(2/10)^4` = `2^4/10^4` = `16/10000` = 0,00016

`0.2^4` = `(1/5)^4` = `1^4/5^4` = `1/3125` = 0,00016


`10^4` = `10*10*10*10` = 10 000

`10^4` = `(2*5)^4` = `2^4*5^4` = `16*625` = 10 000


`0.01^3` = `(1/100)^3` = `1^3/100^3` = `1/1000000` = `1/10^6` = `10^(-6)`

`0.01^3` = `(10^(-2)^3` = `10^(-2*3)` = `10^(-6)`


`50^3` = `50*50*50` = 125 000

`50^3` = `(5*10)^3` = `5^3*10^3` = `125*1000` = 125 000


`8^7` = `8*8*8*8*8*8*8` =

`8^7` = `(2^3)^7` = `2^(3*7)` = `2^(21)`


`0.125^7` = `(125/1000)^7` = `125^7/1000^7`

`0.125^7` = `(1/8)^7` = `1/8^7` = `8^(-7)`

`0.125^7` = `(1/2^3)^7` = `1/(2^(3*7)` = `1/2^(21)` = `2^(-21)`




c,

`(1/5)^3` = `1/5*1/5*1/5` = `(1*1*1)/(5*5*5)` = `1/125`

`(1/5)^3` = `1^3/5^3` = `1/125`


`(4/5)^2` = `4/5*4/5` = `(4*4)/(5*5)` = `16/25`

`(4/5)^2` = `4^2/5^2` = `16/25`


`(3/10)^3` = `(3/10*3/10*3/10` = `(3*3*3)/(10*10*10)` = `27/1000`

`(3/10)^3` = `3^3/10^3` = `27/1000`


d,

`8^4/4^4` = `(8*8*8*8)/(4*4*4*4)` = 16

`8^4/4^4` = `(8/4)^4` = `2^4` = 16


`10^3/5^3` = `(10*10*10)/(5*5*5)` = `1000/125` = 8

`10^3/5^3` = `(10/5)^3` = `2^3` = 8


`1000^2/250^2` = `(1000*1000)/(250*250)` = 16

`1000^2/250^2` = `(1000/250)^2` = `4^2` = 16


`(-7)^5/21^5` = `((-7)*(-7)*(-7)*(-7)*(-7))/(21*21*21*21*21)` = `-1/243`

`(-7)^5/21^5` = `(-7/21)^5` = `(-1/3)^5` = `-1/243`