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

1 Answer
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)