Question

take test: 05: exponential functions hw
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question 9
for positive real number x, 3^{-x}=3^{1/x}.
true
false
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Explanation:

Step1: Recall exponent rule

For any non - zero number \(a\) and real numbers \(m\) and \(n\), \(a^{-m}=\frac{1}{a^{m}}\) and \(a^{m}
eq a^{\frac{1}{m}}\) in general. Here \(a = 3\), \(m=x\). So \(3^{-x}=\frac{1}{3^{x}}\) and \(3^{\frac{1}{x}}=\sqrt[x]{3}\).

Step2: Compare the two expressions

Since \(\frac{1}{3^{x}}
eq\sqrt[x]{3}\) for positive real number \(x\), the equation \(3^{-x}=3^{\frac{1}{x}}\) is false.

Answer:

False