Type a math problem or upload a photo, screenshot, handwritten question...
error msg
- Algebra
- Calculus
- Trigonometry
- Matrix
- Differential
- Integral
- Trigonometry
- Letters
Question
e^{x}xe^{-2}x
Simplify the expression
e^{x-2}x^{2}
Evaluate
e^{x}xe^{-2}x
Multiply the terms with the same base by adding their exponents
e^{x-2}x\times x
Solution
e^{x-2}x^{2}
Show Solutions
Find the roots
x=0
Evaluate
e^{x}xe^{-2}x
To find the roots of the expression,set the expression equal to 0
e^{x}xe^{-2}x=0
Multiply
More Steps
Multiply the terms
e^{x}xe^{-2}x
Multiply the terms with the same base by adding their exponents
e^{x-2}x\times x
Multiply the terms
e^{x-2}x^{2}
e^{x-2}x^{2}=0
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&e^{x-2}=0\\&x^{2}=0\end{align}
\text{Since the left-hand side is always positive,and the right-hand side is always 0,the statement is false for any value of }x
\begin{align}&x \notin \mathbb{R}\\&x^{2}=0\end{align}
The only way a power can be 0 is when the base equals 0
\begin{align}&x \notin \mathbb{R}\\&x=0\end{align}
Solution
x=0
Show Solutions
