`14`
`root [n] ( g ) = g^ (1/n)`
`( g^a )^b = g^(a b)`
`(g^a)/(g^b) = g^ (a - b)`
`(31^25 * root[3](31^30))/(31^12)^3 = (31^25 * 31^(30/3))/(31^(12*3)) = (31^25 * 31^10)/(31^36) = (31^35)/(31^36) = 1/31`
`3^(text(-)2) = 1/(3^2) = 1/9`
`8^(1 2/3) = 8^1 * 8^(2/3) = 8 * (root [3] (8))^2 = 8 * 2^2 = 8*4 = 32`
`4^(text(-)3)=1/(4^3)= 1/64`
`81^(1/4) = root [4] (81) = 3`
`2^(text(-)3)*2^7 = 2^(text(-)3+7) = 2^4 = 16`
`(5^2*5^3)/(25^(1,5)) = (5^2*5^3)/(25^1*25^(1/2)) = (5^2*5^3)/(25*5) = (5^2*5^3)/(5^3) = 5^2 = 25 `
`2 x^(2 1/3) = 2x^2 * x^(1/3) = 2x^2 * root[3](x)`
`(3 x^(text(-)1)) / (2 x) = 3/(2x*x) = 3/(2x^2)`
`4 x^(text(-) 3/4) = 4/(x^(3/4)) = 4/(root[4](x^3))`
`2 x^(2 1/2) = 2x^2 * x^(1/2) = 2x^2 * root[2](x^1) = 2x^2 sqrt(x)`
`1/3 x^(text(-)4) = 1/3 * 1/(x^4) = (1*1)/(3*x^4) = 1/(3x^4)`
`3 x^ (text(-)2 1/2) = 3/(x^(2 1/2)) = 3/(x^2 * x^(1/2)) = 3/(x^2 * sqrt(x))`
`x^(text(-)3/4)`
`(2x)/ ( x sqrt( x )) = 2/sqrt(x) = 2x^(-1/2)`
`5x^(2/3)`
`(x^3 * root [3](x^2))/(4 root[3](x)) = (x^3 *x^(2/3))/(4x^(1/3)) = (x^(3 2/3))/(4x^(1/3)) = 1/4 x^(3 1/3)`
In de exponent staat `2x + 1` . Voor exponentiële groei moet de formule de vorm `y = b*g^x` hebben.
`y=0,5^(2x+1) = 0,5^(2x) * 0,5^1 = (0,5^2)^x * 0,5 = 0,5*0,25^x`
`y=2*3^(2x+2) = 2*(3^2)^x * 3^2 = 18*9^x`
`y=5*0,2^(3x-1) = 5*(0,2^3)^x * 0,2^(text(-)1) = 25*0,008^x`
`y=0,4*5^(text(-2)x+3) = 0,4*(5^(text(-)2))^x * 5^3 = 50*(1/25)^x`
`(2^3)^2 = 2^(3*2) = 2^6 = 64`
`2^3 * 2^2 = 2^(3+2) = 2^5 = 32`
`(2^(1/4))^8 = 2^(1/4*8) = 2^2 = 4`
`root[3](1000) = 1000^(1/3) = (10^3)^(1/3) = 10^(3*1/3) = 10^1 = 10`
`1/(x^2 sqrt(x)) = 1/(x^2*x^(1/2)) = 1/(x^(2 1/2)) = x^(text(-)2 1/2)`
`1/(root[4](x)) = 1/(x^(1/4)) = x^(text(-)1/4)`
`sqrt(x) * x^(text(-)2) = x^(1/2)*x^(text(-)2) = x^(text(-)1 1/2)`
`1/(x sqrt(x)) = 1/(x*x^(1/2)) = 1/x^(1 1/2)=x^(text(-)1 1/2)`
`x^(text(-)1) = 1/(x^1) = 1/x`
`x^(text(-) 1/2) = 1/(x^(1/2)) = 1/(sqrt(x))`
`root [4] ( x^3 )`
`x root[4]( x^3 )`
`3 x^(text(-)1,5)=3/(x^(1,5))=3/ (xsqrt(x))`
`x^(text(-)2,75) = 1/(x^(2,75)) = 1/(x^2*x^(3/4)) = 1/(x^2*root[4](x^3)) = 1/(x^2*root[4](x^3))`
`(17^105)/(17^23) * 17^(text(-)85) = 17^82 * 17^(text(-)85) = 17^(82-85) = 17^(text(-)3) = 1/(17^3)`
`(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`
`(3/4)^231 * (4/9)^230 * 3^233 = 3^231*4^(text(-)231)*4^230*9^(text(-)230)*3^233 = 4^(text(-)1)*3^464*3^(text(-)460) = (3^4)/4=81/4=` `20,25`
`(7^102)/((49^10)^5) = (7^102)/(((7^2)^10)^5) = (7^102)/(7^(2*10*5)) = (7^102)/(7^100) = 7^2 = 49`
`(4/9 * root[3](64))^(1/2) = (4/9)^(1/2)*(root[3](4^3))^(1/2) = (4/9)^(1/2) * 4^(1/2) = sqrt(4/9) * 2 = 2/3 * 2 = 4/3`
`(5^3*(3^5)^15)/(25*root(3)(3^225))= (5^3*3^75)/(5^2*3^75) =5`
`y = (2 x^3)^4 * text(-)3 x^5 = 2^4*x^(3*4) * text(-)3x^5 = 16x^12 * text(-)3x^5 = 16*text(-)3*x^(12+5) = text(-)48x^17`
`y = (2 x * x^2)/(x^6) = (2x^(1+2))/(x^6) = (2x^3)/(x^6) = 2x^(3-6)= 2x^(text(-)3)`
`y = 4 x^2 * root[3](x) = 4x^2 * x^(1/3) = 4x^(2+1/3) = 4x^(2 1/3)`
`y = 2/(x sqrt( x )) = 2/(x^1*x^(1/2)) = 2/(x^(1+1/2)) = 2/x^(1 1/2) = 2x^(text(-)1 1/2)`
`y = 3 * 2^(0,5 x) = 3 * (2^(0,5))^x = 3 * (sqrt(2))^x`
`y = 0,5^(text(-) x + 2) = 0,5^2 * 0,5^(text(-)x) = 0,25 * (0,5^(text(-)1))^x = 0,25 * 2^x`
`y = (1/3)^(3 - 2 x) = (1/3)^3 * (1/3)^(text(-)2x) = 1/27 *((1/3)^(text(-)2))^x = 1/27 * 9^x`
`y = 6 * 2^(4 x - 2) = 6 * 2^(text(-)2) * 2^(4x) = 1,5 *(2^4)^x=1,5*16^x`
In de exponent staat `2x + 1` . Voor exponentiële groei moet de formule de vorm `y = b*g^x` hebben.
`y=4^(text(-)2x+1) = (4^(text(-)2))^x * 4^1 = 4*0,0625^x`
`y = 4^(text(-)2x)+1 = (4^(text(-)2))^x + 1 = 0,0625^x + 1`
Deze formule heeft niet de standaardvorm `y = b*g^x` .
`5^(text(-)1)`
`7^5`
`5^4`
`5^(text(-)1)`
`18 x^10`
`5 x^(text(-)1)`
`3 x^(text(-) 1/2)`
`5 x^( 1 2/5)`
`x*root(4)(x)`
`1/(x^2*sqrt(x))`