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

(7^(log_(7)(2w^(2))))
Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\left(7^{\log _{7}\left(2 w^{2}\right)}\right)$ $\newline$ Answer:

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Full solution

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

\newline

\left(7^{\log _{7}\left(2 w^{2}\right)}\right)

\newline

Answer:

Given Expression: We are given the expression $7^{\log_{7}(2w^{2})}$ . To simplify this expression, we need to use the property of logarithms that states $a^{\log_{a}(b)} = b$ , where a > 0 and $a \neq 1$ .
Property Application: Applying the property to our expression, we get: $\newline$ $7^{\log_{7}(2w^{2})} = 2w^{2}$ $\newline$ This is because the base of the logarithm ( $7$ ) and the base of the exponent ( $7$ ) are the same, so they cancel each other out, leaving us with the argument of the logarithm ( $2w^{2}$ ).
Final Answer: Since there are no further simplifications needed, we have our final answer.

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