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Express the given expression without logs, in simplest form. Assume all variables represent positive values.

(e^(ln(8sqrtw)))
Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\left(e^{\ln (8 \sqrt{w})}\right)$ $\newline$ Answer:

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Simplify radical expressions with variables

Full solution

Q. Express the given expression without logs, in simplest form. Assume all variables represent positive values.

\newline

\left(e^{\ln (8 \sqrt{w})}\right)

\newline

Answer:

Recognize Inverse Functions: We start by recognizing that the natural logarithm function $\ln(x)$ is the inverse of the exponential function $e^x$ . Therefore, when we have $e^{\ln(x)}$ , the two functions cancel each other out, and we are left with just $x$ . This is because $e^{\ln(x)} = x$ for all $x > 0$ .
Apply Inverse Property: Apply the inverse property to the given expression $e^{\ln(8\sqrt{w})}$ . Since $e$ and $\ln$ are inverse functions, $e^{\ln(8\sqrt{w})}$ simplifies to $8\sqrt{w}$ .
Simplify Expression: Now we have the simplified expression $8\sqrt{w}$ , which is already in its simplest form. There is no further simplification needed.

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