Question

How do you simplify \[3{{a}^{2}}{{b}^{-3}}\]?

Answer 1

Hint: Simplification of an algebraic equation is usually done by using the various algebraic formulae fitting for different scenarios. The given expression more or less is already in the simplified form, we can just rearrange the variables involved in the expression.
For example - If the question is to simplify \[{{(2x+y)}^{2}}\], then we use the formula \[(a+b)={{a}^{2}}+2ab+{{b}^{2}}\] to simplify the expression.

Complete step-by-step solution:
According to the question, we have to simplify \[3{{a}^{2}}{{b}^{-3}}\]
The given expression is already in the simplified form so more or less it can only be rearranged.
So the given expression can be written also as:
\[3{{a}^{2}}{{b}^{-3}}\]
\[\Rightarrow \dfrac{3{{a}^{2}}}{{{b}^{3}}}\]
The new form obtained is not actually a new form or a simplification. Rather the expression given to us was one way to write this \[\dfrac{3{{a}^{2}}}{{{b}^{3}}}\]. Since this cannot be simplified further nor can be converted to any other simplified form. The question itself is a simplified version. So the answer to the question is the question itself, since we just wrote the expression given to us in another form and not any specific simplification.
The simplified form of the expression is \[\dfrac{3{{a}^{2}}}{{{b}^{3}}}\].

Note: The expressions that are given to us for simplification are in some or the other form related to some specific algebraic formulae. We just need to perceive it in the form of some related formula. Even if the expression cannot be viewed in relation to any formulae in specific, we can always try to convert it to some form by using the basic arithmetic operations on the expression.