Simplify e^(-3ln 2+2) and write without any logarithms. Answer:

Apply Power Rule: Apply the power rule of logarithms to the term -3ln(2). The power rule states that a*log_b(c) = log_b(c^a), so we can rewrite -3ln(2) as ln(2^(-3)).Simplify Using Property: Simplify the expression using the property of logarithms. e^(ln(a)) = a, so we can simplify e^(ln(2^(-3))) to 2^(-3).Combine Simplified Terms: Combine the simplified term with the remaining part of the exponent. We have e^(ln(2^(-3))) * e^(2), which simplifies to 2^(-3) * e^(2).Simplify 2^(-3): Simplify the term 2^(-3). 2^(-3) is the same as 1/(2^3), which equals 1/8.Combine Final Answer: Combine the simplified terms to get the final answer. The final expression is (1/8) * e^(2).

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Simplify
e^(-3ln 2+2) and write without any logarithms.
Answer:

Simplify $e^{-3 \ln 2+2}$ and write without any logarithms. $\newline$ Answer:

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Math Problems

Algebra 2

Evaluate rational exponents

Full solution

Q. Simplify

e^{-3 \ln 2+2}

and write without any logarithms.

\newline

Answer:

Apply Power Rule: Apply the power rule of logarithms to the term $-3\ln(2)$ . $\newline$ The power rule states that $a\log_b(c) = \log_b(c^a)$ , so we can rewrite $-3\ln(2)$ as $\ln(2^{-3})$ .
Simplify Using Property: Simplify the expression using the property of logarithms. $e^{\ln(a)} = a$ , so we can simplify $e^{\ln(2^{-3})}$ to $2^{-3}$ .
Combine Simplified Terms: Combine the simplified term with the remaining part of the exponent. $\newline$ We have $e^{\ln(2^{-3})} \times e^{2}$ , which simplifies to $2^{-3} \times e^{2}$ .
Simplify $2^{-3}$ : Simplify the term $2^{-3}$ . $2^{-3}$ is the same as $1/(2^3)$ , which equals $1/8$ .
Combine Final Answer: Combine the simplified terms to get the final answer. $\newline$ The final expression is $(\frac{1}{8}) \times e^{2}$ .