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Which of the following statements are true? Select all that apply. e^2.2=e^(11)/(5) (1)/(e)=(e^-10)/(e^-9) 1^e=e e^-(1)/(2)=(1)/(sqrt (e)) -(e^frac (3)/(4))(e^(1)/(2))=-sqrt [4](e) -e^3=(1)/(e^-3)

Pergunta

Which of the following
statements are true?
Select all that apply.
e^2.2=e^(11)/(5)
(1)/(e)=(e^-10)/(e^-9)
1^e=e
e^-(1)/(2)=(1)/(sqrt (e))
-(e^frac (3)/(4))(e^(1)/(2))=-sqrt [4](e)
-e^3=(1)/(e^-3)

Which of the following statements are true? Select all that apply. e^2.2=e^(11)/(5) (1)/(e)=(e^-10)/(e^-9) 1^e=e e^-(1)/(2)=(1)/(sqrt (e)) -(e^frac (3)/(4))(e^(1)/(2))=-sqrt [4](e) -e^3=(1)/(e^-3)

Solução

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BárbaraMestre · Tutor por 5 anos

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Let's analyze each statement one by one:<br /><br />1. $e^{2.2}=e^{\frac {11}{5}}$: This statement is true. We can rewrite $2.2$ as $\frac{11}{5}$, so $e^{2.2}$ is equal to $e^{\frac {11}{5}}$.<br /><br />2. $\frac {1}{e}=\frac {e^{-10}}{e^{-9}}$: This statement is true. We can simplify the right side of the equation by using the property of exponents: $e^{-10} \cdot e^{-9} = e^{-19}$. Therefore, $\frac {e^{-10}}{e^{-9}} = e^{-10} \cdot e^{9} = e^{-1} = \frac {1}{e}$.<br /><br />3. $1^{e}=e$: This statement is false. Any number raised to the power of $e$ is not equal to $e$. In this case, $1^e$ is equal to $1$, not $e$.<br /><br />4. $e^{-\frac {1}{2}}=\frac {1}{\sqrt {e}}$: This statement is true. We can rewrite $e^{-\frac {1}{2}}$ as $\frac{1}{e^{\frac{1}{2}}}$, which is equal to $\frac{1}{\sqrt{e}}$.<br /><br />5. $-\frac {e^{\frac {3}{4}}}{e^{\frac {1}{2}}}=-\sqrt [4]{e}$: This statement is false. We can simplify the left side of the equation by using the property of exponents: $-\frac {e^{\frac {3}{4}}}{e^{\frac {1}{2}}} = -e^{\frac {3}{4} - \frac {1}{2}} = -e^{\frac {1}{4}}$. This is not equal to $-\sqrt [4]{e}$.<br /><br />6. $-e^{3}=\frac {1}{e^{-3}}$: This statement is false. We can rewrite the right side of the equation as $e^{3}$, so $-e^{3}$ is not equal to $e^{3}$.<br /><br />Therefore, the true statements are:<br />- $e^{2.2}=e^{\frac {11}{5}}$<br />- $\frac {1}{e}=\frac {e^{-10}}{e^{-9}}$<br />- $e^{-\frac {1}{2}}=\frac {1}{\sqrt {e}}$
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