ExponentiÃ«le functies > Exponenten en machten
123456Exponenten en machten

## Antwoorden van de opgaven

Opgave V1

19

Opgave 1
a

root[n](g)=g^ (1/n)

b

(g^a) ^b=g^ (ab)

c

g^a/(g^b)=g^ (a-b)

Opgave 2
a

(31^25*root[3] (31^30)) /((31^12) ^3)=(31^25*(31^30)^(1/3))/(31^(12*3))=(31^(25+10))/(31^36)=1/31

b

(25^4*(5^5)^9)/(root [4](5^40)*125^14)=((5^2)^4*5^45)/((5^(40))^(1/4)*(5^3)^(14))=(5^8*5^45)/(5^10*5^42)=(5^53)/(5^52)=5

Opgave 3
a

3^(text(-)2)=1/(3^2)=1/9

b

81^(1/4)=(3^4)^(1/4)=3

c

8^(1 2/3)=8^(5/3)=8*8^(2/3)=8*(2^3)^(2/3)=32

d

2^(text(-)3)*2^7=2^(text(-)3+7)=2^4=16

e

(3^(text(-)12))^(1/4)=3^(text(-)3)=1/27

f

(2^ (1/2)) ^10=2^5=32

Opgave 4
a

2 x^ (2 1/3)=2x^2*x^(1/3)=2 x^2*root3 (x)

b

(3 x^(text(-)1)) / (2 x)=3*1/x * 1/(2x)=3/(2x^2)

c

4 x^(text(-)3/4)=4*1/(x^(3/4)) = 4/(root[4] (x^3))

d

2 sqrt(x)

Opgave 5
a

3/(2x)=3/2 * 1/x = 1,5x^(text(-)1)

b

3/ (2 xsqrt(x))=3/(2x^(1 1/2))=1,5x^(text(-)1 1/2)

c

(4 root[3] (x)) ^2=(4*x^(1/3))^2=4^2*(x^(1/3))^2=16x^(2/3)

d

2x sqrt(x)=2x*x^(1/2)=2x^(1 1/2)

e

2/ (x^3*root[3] (x^2))=2*x^(text(-)3)*x^(text(-)2/3)=2 x^ (text(-)3 2/3)

f

3 x^5* (2 x^3) ^2=3x^5*2^2*x^6=12x^11

Opgave 6

12 *3^ (text(-)0,5 x+1) =12 *3^ (text(-)0,5 x) *3^1=12 *3 * (3^(text(-)0,5)) ^x=36 * (1/ sqrt(3 ) ) ^x

b=36 en g=1/ sqrt(3 ) .

Opgave 7
a

(2^3) ^2=2^6=64

b

2^5=32

c

2^2=4

d

(10^3) ^ (1/3) =10^1=10

Opgave 8
a

x^(text(-)1/2)=1/x^(1/2)=1/sqrt(x)

b

root4 (x^3)

c

3x^(text(-)1,5)=3*1/(x^1,5)=3/(xsqrt(x))

d

1/2x^(text(-)2,75)=1/2*1/(x^(2,75))=1/2*1/(x^(2 3/4))=1/2*1/(x^2*root[4](x^3))=1/ (2 x^2root[4] (x^3))

Opgave 9
a

1/ (x^2sqrt(x))=1/x^(2,5)=x^(text(-)2,5)

b

1/ (3 *root4 (x))=1/3*1/root4(x)=1/3*1/x^(1/4)=1/3*x^(text(-)1/4)

c

1/ (2 xsqrt(x))=1/(2x^(1,5))=1/2*x^(text(-)1 1/2)

d

(3 xsqrt(x)) ^3=(3*x^(1,5))^3=3^3*x^(4 1/2)=27x^(4 1/2)

Opgave 10
a

(17^105)/(17^22)*17^(text(-)85)=17^83*17^(text(-)85)=17^(text(-)2)=1/17^2=1/289

b

(1/2) ^219*8^72=(2^(text(-)1))^219*(2^3)^72=2^(text(-)219)*2^216=2^(text(-)3)=1/2^3=1/8

c

(3/4)^231* (4/9)^230*3^233=(3^231)/(4^231)*(4^230)/(9^230)*3^233=(4^230)/(4^231)*(3^231)/(3^460)*3^233=1/4* 3^4=20 1/4

d

(7^102)/((49^10) ^5)=(7^102)/(((7^2)^10)^5)=(7^102)/(7^100)=7^2=49

e

(4/9*root[3](64))^(1/2)=(4/(9)*root[3](4^3))^(1/2)=(4/9*4)^(1/2)=(16/9)^(1/2)=4/3

f

(5^3*(3^5)^15)/(25*root(3)(3^225))= (5^3*3^75)/(5^2*3^75) =5

Opgave 11
a

(2 x^3) ^4*text(-)3 x^5=2^4*x^12*text(-)3x^5=text(-)48 x^17

b

(2 x*x^2) /x^4=(2x^3)/x^3=2 x^(text(-)1)

c

(3x^2*root3 (x))/(9x^3*x^(2/3)) =(3*x^2*x^(1/3))/(3^2*x^3*x^(2/3)) =(3*x^(7/3)) / (3^2*x^(11/3))=1/3 x^(text(-)4/3)

d

(2x^(1 1/2))^3/ (xsqrt(x)) =(8*x^(4 1/2))/ (x^(1 1/2))= 8x^3

e

1/2x^ (text(-)1 1/3) *root(4)(x) = 1/2 * x^(text(-)4/3) * x^(1/4) = 1/2 * x^(text(-)16/12) * x^(3/12)= 1/2x^(text(-)13/12)

f

(12x^(1 2/5))/(6x^(text(-)3/5))+2x^2= (12 x ^(7/5))/ (6x^(text(-)3/5)) + 2x^2 = 2x^2+2x^2=4x^2

Opgave 12
a

f(x)=3*2^(0,5x)=3*(2^(0,5))^x=3*(sqrt(2))^x

b

f(x)=0,5^(text(-)x+2)=0,5^(text(-)1*x)*0,5^2=(0,5^(text(-)1))^x* 0,25=0,25*2^x

c

f(x)=9*(1/3)^(4-2x)=3^2*(3^(text(-)1))^4*((3^(text(-)1))^(text(-)2))^x=1/9*9^x

d

f(x)=7*5^(2x+1)+2*(sqrt(5))^(4x)=7*(5^2)^x*5+2*((sqrt(5))^4)^x=35*25^x+2*25^x=37*25^x .

Opgave 13Priemfactoren
Priemfactoren
a

26=2*13
25=5^2
144=2^4*3^2
127=127
202=2*101

b
• ((126)^2*(3773))/(sqrt(81)*343*693)=((2*3^2*7)^2*7^3*11)/(3^2*7^3*3^2*7*11)=(2^2*3^4*7^5*11)/(3^4*7^4*11)=28

• ((5)^(text(-)2)*(19600)^(1/2))/(91)=((5)^(text(-)2)*(2^4*5^2*7^2)^(1/2))/(7*13)=(2^2*5^(text(-)1)*7)/(7*13)=4/(5*13)=4/65

• ((1080)^(1/3)*sqrt(5^(4/3)))/((1296)^(1/4))=((2^3*3^3*5)^(1/3)*(5^(4/3))^(1/2))/(2^4*3^4)^(1/4)=(2*3*5^(1/3)*5^(2/3))/(2*3)=5^(1/3+2/3)=5

Opgave 14
a

3^(text(-)1)=1/3

b

2^5=32

c

2^4=16

d

3^(text(-)1)=1/3

Opgave 15
a

1/sqrt(x)

b

x*root(10)(x^3)

Opgave 16
a

0,3 x^(text(-)1)

b

1/4x^(1,5)

c

1,5 x^ (text(-)1 1/2)

Opgave 17

f(x)=12sqrt(3) *3^x