To rewrite the expression \(\dfrac{12\sqrt x}{4x^3}\) in the form \(k \cdot x^n\), we can simplify it further.
First, let's simplify the numerator. The square root of \(x\) can be written as \(x^{1/2}\). So, we have:
\(\dfrac{12x^{1/2}}{4x^3}\)
Next, let's simplify the denominator. We can rewrite \(x^3\) as \(x^{3/1}\). So, we have:
\(\dfrac{12x^{1/2}}{4x^{3/1}}\)
Now, let's simplify the expression by dividing the coefficients and subtracting the exponents of \(x\):
\(\dfrac{12}{4} \cdot x^{(1/2) - (3/1)}\)
Simplifying further, we have:
\(3 \cdot x^{-5/2}\)
So, the expression \(\dfrac{12\sqrt x}{4x^3}\) can be rewritten as \(3 \cdot x^{-5/2}\).
If you have any more questions or need further clarification, feel free to ask!