# How do you simplify #(x^(3/2))/(3/2)#?

##### 1 Answer

#### Explanation:

The most important thing to know here is that **dividing by a fraction** is equivalent to **multiplying by the fraction's reciprocal.**

The expression we have here can be written as:

#=x^(3/2)-:3/2#

Instead of dividing by the fraction

#=x^(3/2)xx2/3#

This can be written as

#=(2x^(3/2))/3#

This is a *fine* simplification. However, if you want to simplify the fractional exponent, we can use the rule which states that

#x^(a/b)=rootb(x^a)#

Thus, the expression equals

#=(2root2(x^3))/3=(2sqrt(x^3))/3#

We could simplify

#=(2xsqrtx)/3#

This really becomes a matter of opinion as to where you wish to stop simplifying.