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$Express the given expression as an integer or as a fraction in simplest form. (2^(log_(2)((1)/(3)))) Answer:$

Express the given expression as an integer or as a fraction in simplest form. $\newline$ $\left(2^{\log _{2} \frac{1}{3}}\right)$ $\newline$ Answer:

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Operations with rational exponents

Full solution

Q. Express the given expression as an integer or as a fraction in simplest form.

\newline

\left(2^{\log _{2} \frac{1}{3}}\right)

\newline

Answer:

Understand the expression: Understand the expression $2^{\log_{2}\left(\frac{1}{3}\right)}$ . The expression represents $2$ raised to the power of the base- $2$ logarithm of $\frac{1}{3}$ . The base- $2$ logarithm of a number is the power to which $2$ must be raised to obtain that number.
Apply logarithm property: Apply the property of logarithms that states $a^{\log_{a}(b)} = b$ . Here, $a$ is $2$ and $b$ is $\frac{1}{3}$ . Therefore, $2^{\log_{2}(\frac{1}{3})}$ simplifies to $\frac{1}{3}$ .
Express as fraction: Express the result as a fraction in simplest form. $\newline$ The result from Step $2$ is already a fraction in simplest form, which is $\frac{1}{3}$ .

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