bewerking=nivo/bewerking6.proc
#bewerking=$commondir/number.proc
#varlist=x
plaatje=0
!set n=$teller
!if $graad =0
    R=$teller
!else
    R=$graad
!endif        
nivo_title=!record 19 of lang/remarks.$taal
somtekst$n=!record 62 of lang/remarks.$taal

!if $R=1
    # 1/a*x^-b = 1/c
    # 1/(a*x^b)=1/c
    # ax^b=c
    # x^b=c/a => x=(c/a)^(1/b)
    a=!randitem 2,3,4,5,6
    f=!randitem 2,3,4,5
    exp=$[-1*($teller+1)]
    b=$[-1*$exp]
    c=$[$f*$a]
    x=$f^(1/$b)
    xx=$f^{1/$b}
    opgave$n=\frac{1}{$a} \cdot x^{$exp} = \frac{1}{$c}
    !if $[gcd($exp,2)]=2
    	#even
	GOED$n=$x,-$x
	goed$n=\rightarrow \frac{1}{$a \cdot x^{$b}}= \frac{1}{$c} \rightarrow $a \cdot x^{$b} = $c \rightarrow x = \root $b \of{$f} = $xx \vee -$xx
    !else
	#oneven
	GOED$n=$x
	goed$n=\rightarrow \frac{1}{$a \cdot x^{$b}} = \frac{1}{$c} \rightarrow $a \cdot x^{$b} = $c \rightarrow x = \root $b \of{$f} = $xx 
    !endif
 !exit
!endif 

!if $R=2
    # e/(e*a)*x^-b= 1/c => 1/a*x-b =1/c 
    e=!randitem 2,3,4,5
    a=!randitem 2,3,4,5,6
    f=!randitem 2,3,4,5
    exp=$[-1*($teller+1)]
    b=$[-1*$exp]
    c=$[$f*$a]
    x=$f^(1/$b)
    xx=$f^{1/$b}
    opgave$n=\frac{$e}{$[$e*$a]} \cdot x^{$exp} = \frac{1}{$c}
    !if $[gcd($exp,2)]=2
    	#even
	GOED$n=$x,-$x
	goed$n=\rightarrow \frac{1}{$a \cdot x^{$b}}= \frac{1}{$c} \rightarrow $a \cdot x^{$b} = $c \rightarrow x = \root $b \of{$f} = $xx \vee -$xx
    !else
	#oneven
	GOED$n=$x
	goed$n=\rightarrow \frac{1}{$a \cdot x^{$b}} = \frac{1}{$c} \rightarrow $a \cdot x^{$b} = $c \rightarrow x = \root $b \of{$f} = $xx 
    !endif
    
 !exit
!endif 

!if $R>2
    # e/a*x^-b = e*e/c*e
    # 1/(a*x^b)=1/c
    # ax^b=c
    # x^b=c/a => x=(c/a)^(1/b)
    e=!randitem 2,3,4
    p=!randitem 1,2,3,4
    a=$[$e+$p]
    f=!randitem 2,3,4,5
    exp=$[-1*($teller+1)]
    b=$[-1*$exp]
    c=$[$f*$a]
    x=$f^(1/$b)
    xx=$f^{1/$b}
    opgave$n=\frac{$e}{$a} \cdot x^{$exp} = \frac{$[$e*$e]}{$[$c*$e]}
    !if $[gcd($exp,2)]=2
    	#even
	GOED$n=$x,-$x
	goed$n=\rightarrow \frac{1}{$a \cdot x^{$b}}= \frac{1}{$c} \rightarrow $a \cdot x^{$b} = $c \rightarrow x = \root $b \of{$f} = $xx \vee -$xx
    !else
	#oneven
	GOED$n=$x
	goed$n=\rightarrow \frac{1}{$a \cdot x^{$b}} = \frac{1}{$c} \rightarrow $a \cdot x^{$b} = $c \rightarrow x = \root $b \of{$f} = $xx 
    !endif
 !exit
!endif 

