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

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Answer 1 · 2016-02-16T21:26:01

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

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.

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