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

Answer 1

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

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 #"3/2"#, we can instead multiply by its reciprocal, #"2/3"#.

#=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 #sqrt(x^3)# by saying that #sqrt(x^3)=sqrt(x^2)sqrtx=xsqrtx#.

#=(2xsqrtx)/3#

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

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.