Question

How do you simplify \[4{{c}^{-3}}\] ?

Answer 1

Hint: we can solve this using the exponent concept. We have to make the negative exponent as positive using the formula and then we have to simplify it further to get the simplified form of the given equation. For solving this type of questions we have to know the formulas of exponents.

Complete step by step answer:
First we have to know some basic identities of exponents.
\[{{a}^{0}}=1\]
\[{{a}^{1}}=a\]
\[{{a}^{-n}}=\dfrac{1}{{{a}^{n}}}\]
\[{{a}^{n}}=\dfrac{1}{{{a}^{-n}}}\]
\[{{a}^{m}}{{a}^{n}}={{a}^{m+n}}\]
These are some of the important formulas of exponents. We will use some of them in simplifying the given expression.
Given expression is
\[4{{c}^{-3}}\]
First we have to make the negative expression as positive. For this we have formula above
 \[{{a}^{-n}}=\dfrac{1}{{{a}^{n}}}\]
Using this formula we can write \[{{c}^{-3}}\] as \[\dfrac{1}{{{c}^{3}}}\]. Then the equation will look like
\[\Rightarrow 4\times \dfrac{1}{{{c}^{3}}}\]
Now we can multiply the expression to get the result
\[\Rightarrow \dfrac{4}{{{c}^{3}}}\]
We cannot simplify it further. So this is the simplest form that we can get from the given equation.
 The simplest form of the \[4{{c}^{-3}}\] is \[\dfrac{4}{{{c}^{3}}}\].

Note: We can also make it simple by leaving the negative power as it is and simplifying \[4\].
We can write \[4\] as \[{{2}^{2}}\].
Then the expression will look like
\[\Rightarrow {{2}^{2}}{{c}^{-3}}\]
But this method is not recommended because \[{{c}^{-3}}\] is not a simplified form. It is always recommended to have positive signs in powers. If there is a negative sign try to change it to positive.
But we have to be sure while applying the formulas. We have to be specific about using formulas to get the solution.