Simplify e^(-2ln 3) Answer:

Recognize Properties: Recognize the properties of logarithms and exponents. We have the expression e^(-2ln 3). The property of logarithms that we can use here is that e^(ln x) = x for any x > 0. We can apply this property in reverse to simplify our expression.Apply Power Rule: Apply the power rule for logarithms. The power rule for logarithms states that a*ln(b) = ln(b^a). We can apply this rule to our expression to simplify it. e^(-2ln 3) = e^(ln(3^(-2)))Simplify Using Property: Simplify using the property of e and the natural logarithm. Using the property that e^(ln x) = x, we can simplify our expression further. e^(ln(3^(-2))) = 3^(-2)Calculate Value: Calculate the value of 3^(-2). 3^(-2) means 1 divided by 3 squared. 3^(-2) = 1/(3^2) = 1/9

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Simplify $e^{-2 \ln 3}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Simplify

e^{-2 \ln 3}

\newline

Answer:

Recognize Properties: Recognize the properties of logarithms and exponents. $\newline$ We have the expression $e^{(-2\ln 3)}$ . The property of logarithms that we can use here is that $e^{(\ln x)} = x$ for any x > 0. We can apply this property in reverse to simplify our expression.
Apply Power Rule: Apply the power rule for logarithms. $\newline$ The power rule for logarithms states that $a\ln(b) = \ln(b^a)$ . We can apply this rule to our expression to simplify it. $\newline$ $e^{(-2\ln 3)} = e^{(\ln(3^{-2}))}$
Simplify Using Property: Simplify using the property of $e$ and the natural logarithm. $\newline$ Using the property that $e^{\ln x} = x$ , we can simplify our expression further. $\newline$ $e^{\ln(3^{-2})} = 3^{-2}$
Calculate Value: Calculate the value of $3^{-2}$ . $3^{-2}$ means $1$ divided by $3$ squared. $3^{-2} = 1/(3^2) = 1/9$