Simplify e^((1)/(3)ln 125) Answer:

Identify Base and Exponent: Identify the base and the exponent in e^((1)/(3)ln 125). In e^((1)/(3)ln 125), Base: e Exponent: (1)/(3)ln 125Use Exponent Property: Use the property of exponents that e^(ln x) = x to simplify the expression. Since ln 125 is the natural logarithm of 125, we can rewrite the expression as: e^((1)/(3)ln 125) = (e^(ln 125))^(1/3)Simplify Using Property: Simplify the expression using the property from Step 2. e^(ln 125) = 125 So, (e^(ln 125))^(1/3) = 125^(1/3)Calculate Cube Root: Calculate the cube root of 125. 125 is 5 cubed, so the cube root of 125 is 5. 125^(1/3) = 5

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Simplify $e^{\frac{1}{3} \ln 125}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Simplify

e^{\frac{1}{3} \ln 125}

\newline

Answer:

Identify Base and Exponent: Identify the base and the exponent in $e^{\left(\frac{1}{3}\ln 125\right)}$ . $\newline$ In $e^{\left(\frac{1}{3}\ln 125\right)}$ , $\newline$ Base: $e$ $\newline$ Exponent: $\left(\frac{1}{3}\ln 125\right)$
Use Exponent Property: Use the property of exponents that $e^{\ln x} = x$ to simplify the expression. $\newline$ Since $\ln 125$ is the natural logarithm of $125$ , we can rewrite the expression as: $\newline$ $e^{(1)/(3)\ln 125} = (e^{\ln 125})^{1/3}$
Simplify Using Property: Simplify the expression using the property from Step $2$ . $\newline$ $e^{\ln 125} = 125$ $\newline$ So, $(e^{\ln 125})^{\frac{1}{3}} = 125^{\frac{1}{3}}$
Calculate Cube Root: Calculate the cube root of $125$ . $125$ is $5$ cubed, so the cube root of $125$ is $5$ . $125^{(1/3)} = 5$