Question

How do you simplify \[\dfrac{3e}{{{e}^{x}}}\]?

Answer 1

Hint: In this problem, we have to simplify the given exponential expression. We can use laws of exponent to simplify this problem. We know that we have many rules of exponentiation, but here we are going to use dividing powers with the same base. We should know that in division if bases are the same then we need to subtract the exponents. In the multiplication rule of exponent, if we have the same base of two numbers, then we can add the power.

Complete step by step answer:
We know that the given exponential expression to be simplified is,
\[\dfrac{3e}{{{e}^{x}}}\]…… (1)
We also know that the law of exponent for division can be used in this problem.
Here we are going to use dividing power with the same base.
We should know that in division if bases are same then we need to subtract the exponents,
\[\dfrac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}}\]
We can write the expression (1) as,
\[\Rightarrow 3\left( \dfrac{e}{{{e}^{x}}} \right)\]
Now we can apply the division law of exponent, we get
\[\begin{align}
  & \Rightarrow 3\left( {{e}^{1-x}} \right) \\
 & \Rightarrow 3{{e}^{1-x}} \\
\end{align}\]

Therefore, the simplified form of \[\dfrac{3e}{{{e}^{x}}}\] is \[3{{e}^{1-x}}\].

Note: Students make mistakes while writing the correct law of exponent. We should know the law of exponent or rules of exponent to simplify these types of problems. In the division rule of exponent, if we have the same base in the numerator and the denominator, then we can subtract the power, in the multiplication rule of the exponent, if we have the same base of two numbers, then we can add the power.