Question

Simplify
`{({4e}^( - 8x))}^(0.5)`with no negative exponents. thanks!

Answer 1

`\text{Answer : }(2)/(e^(4x))`

Step-by-step explanation

Given the following expression

`\begin{gathered} \text{Simplify (4 }e^(-8x))^{(1)/(2)} \\ \text{This expression can be written as} \\ (4\cdot\text{ }e^(-8x))^{(1)/(2)} \\ \text{Splitting the expression, we can have the below expression} \\ (4)^{(1)/(2)}\cdot(^{}e^(-8x))^{(1)/(2)} \\ \text{According to the law of indicies} \\ x^{(1)/(2)}\text{ = }\sqrt[]{x} \\ \text{Hence, we have the following expression} \\ \sqrt[]{4\text{ }}\cdot\text{ (}e^{-8x\cdot\text{ }(1)/(2)}) \\ 2\cdot\text{ }e^(-4x) \\ 2e^(-4x) \\ \text{Therefore, the simplified form is 2}e^(-4x) \\ (2)/(e^(4x)) \end{gathered}`