How do you simplify #r^(1/2)/(r^(-1/4))#?

1 Answer
Sheffy
Jun 4, 2016

#r^(3/4)#

Explanation:

#r^(1/2)/r^(-1/4)=r^(1/2)-:r^(-1/4) #

Here, since the #color(red)("bases are same")#, and we have to find the #color(red)("divide the terms")#, we can simply #color(red)("SUBTRACT THE POWERS")#:

#r^(1/2)-:r^(1/4) = r^(1/2-(-1/4)) #

#= r^(1/2+1/4) #

#=r^((2+1)/4)#

#=r^(3/4)#

ALTERNATELY

We know that:

#x^-n=1/x^n#

Therefore,

#1/x^-n=1/(1/x^n)=x^n#

#=>1/r^(-1/4) = r^(1/4)#

The given expression can be written as:

#r^(1/2)xxr^(1/4)#

Here, since the #color(red)("bases are same")#, and we have to find the #color(red)("multiply the terms")#, we can simply #color(red)("ADD THE POWERS")#:

#r^(1/2)xxr^(1/4)=r^(1/2+1/4)#

#=r^((2+1)/4)#

#=r^(3/4)#

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