Simplify e^(2ln 9) Answer:

Understand Properties: Understand the properties of logarithms and exponents. The expression e^(2ln 9) involves the natural logarithm ln and the natural exponential function e. The property that we can use here is that e^(ln x) = x for any positive number x. This is because ln is the inverse function of e^x.Apply Power Rule: Apply the power rule for logarithms. The power rule for logarithms states that a logarithm of a power, such as ln(x^y), can be written as y * ln(x). In our case, we have 2ln(9), which can be rewritten as ln(9^2).Simplify Using Property: Simplify the expression using the property of e and ln. Now we can use the property from Step 1 to simplify e^(ln(9^2)). Since e and ln are inverse functions, e^(ln(9^2)) simplifies to just 9^2.Calculate Value: Calculate the value of 9^2. 9^2 is 9 multiplied by itself, which equals 81.

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Simplify $e^{2 \ln 9}$ $\newline$ Answer:

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Algebra 1

Evaluate integers raised to positive rational exponents

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Q. Simplify

e^{2 \ln 9}

\newline

Answer:

Understand Properties: Understand the properties of logarithms and exponents. $\newline$ The expression $e^{2\ln 9}$ involves the natural logarithm $\ln$ and the natural exponential function $e$ . The property that we can use here is that $e^{\ln x} = x$ for any positive number $x$ . This is because $\ln$ is the inverse function of $e^x$ .
Apply Power Rule: Apply the power rule for logarithms. The power rule for logarithms states that a logarithm of a power, such as $\ln(x^y)$ , can be written as $y \cdot \ln(x)$ . In our case, we have $2\ln(9)$ , which can be rewritten as $\ln(9^2)$ .
Simplify Using Property: Simplify the expression using the property of $e$ and $\ln$ . Now we can use the property from Step $1$ to simplify $e^{\ln(9^2)}$ . Since $e$ and $\ln$ are inverse functions, $e^{\ln(9^2)}$ simplifies to just $9^2$ .
Calculate Value: Calculate the value of $9^2$ . $9^2$ is $9$ multiplied by itself, which equals $81$ .