Rekenen II > MachtenAntwoorden van de opgaven
`920` m
`b+b+a+b+2a+a`
`PS = 4a+3b`
`L = 6a + 4b`
`L= 6*80 + 4*200 = 1280` m
`A = 3a^2 + b^2 + ab`
`A = 3*80^2 + 200^2 + 80*200 = 75200` m2
`1`
`42,875`
`1/81`
`16/625`
`81`
`( text(-)3 ) ^4 = text(-)3 * text(-)3 * text(-)3 *text(-)3 = 81`
`text(-)3^4 = text(-)3 * 3 * 3 * 3 = text(-)81`
`1/16`
`18 26/27`
`1`
`text(-)18`
`3^95 * 3^114 = 3^209`
`(3^114)/(3^95) = 3^19`
`( 3^12 )^5 = 3^60`
`1`
`4 * 32 - 400/(16) = 103`
`((8 + 9)^2)/17 - 4 = 17 - 4 = 13`
`(2*1/8)^3 = (1/4)^3 = 1/64`
`500 - text(-)5*5*5 = 625`
`500 - text(-)5*text(-)5*text(-)5 = 625`
`500 + text(-)5*5*5*5 = text(-)125`
`500 + text(-)5*text(-)5*text(-)5*text(-)5 = 1125`
`(13^240)/((13^10)^4 * 13^200) = (13^240)/(13^40 * 13^200) = 1` .
`(4^99)/(2^150 * (text(-)2^5)^10) = ((2^2)^99)/(2^150 * 2^50) = (2^198)/(2^200) = 1/(2^2) = 1/4` .
`(1,20*10^6) // (42*10^3) = 1,20 // 42 *10^3 ~~ 28,6` uur.
`12 // (6,02*10^23) ~~ 1,99 * 10^(text(-)23) ~~ 19,9 * 10^(text(-)24)` gram.
`4^5 = 1024`
`3^4 * 2^3 = 648`
`( 2/3 )^4 = 16/81`
`( 1 3/5 )^3 = 4 12/125`
`( text(-)2 )^6 = 64`
`text(-)2^4 * 3^3 = text(-)432`
`2^16 * ( 2^10 ) ^3 = 2^46`
`(4 * 2^26)/(2^20) = 2^8`
`(2^14 * 2^26)/((2^20)^2) = 2^0 = 1`
`12 * 1,66 * 10^(text(-)24) = 19,92 * 10^(text(-)24) ~~ 1,99 * 10^(text(-)23)` gram.
Uit ongeveer `(12)/(1,99 * 10^(text(-)23)) ~~ 6,02 * 10^(23)` atomen. (Dit getal is de constante van Avogadro.)
Allebei ongeveer `6,02 * 10^23` atomen.
Ongeveer `(10^3)/(18 * 1,66 * 10^(text(-)24)) ~~ 3,35 * 10^25` .
`1/(150*10^6) ~~ 6,7*10^(text(-)9)` AE. (Denk er om dat je antwoorden ook in de technische notatie moeten staan en dat veel decimalen of exacte waarden nu onzinnig zijn.)
`5,2*150*10^6 = 780*10^6` km.
`(5,9*10^9)/(150*10^6) ~~ 39` AE.
Het licht legt in een jaar ongeveer `365 * 24 * 60 * 60 * 300*10^6 // 1000 ~~ 9,46*10^12` km af. Dat is ongeveer `63072` AE.
Volume `V = a*a*a = a^3`
`G = a^3*10,5`
Het volume is
`64`
cm3.
Het gewicht is
`672`
gram
Het volume is `8^3 = 512 ` cm3. Het gewicht is `8^3*10,5 = 5367` gram
Volume `V = a*2a*2a = 4a^3` . Gewicht `G = 4a^3 * 10,5`
Indien
`a = 4`
cm:
`V = 256`
cm3 en
`G = 2688`
g.
Indien
`a = 8`
cm:
`V = 2048`
cm3 en
`G = 21504`
g.
`N = 180000* 0,88^t`
`N = 180000 * 0,88^19 = 15865`
`2^7 = 128`
`(text(-)2)^7 = text(-)128`
`text(-)2^7 = text(-)128`
`(2/3)^4 = 16/81`
`3^6 = 729`
`text(-)4*2^3 - (3/4)^3 = text(-)32 27/64`
`text(-)2*(text(-)4)^4 = text(-)512`
`(2/4)^3*3 + 2^6 = 64 3/8`
`text(-)4^4 + 3^5*2^2 = 716`
`(9^20)^4/(3^2*9^16) = 9^63`
`6^16*6^12 = 6^28`
`(4^17)^4 = 4^68`
`12^14*12^80/12^56 = 12^38`