If 3^(a)=root(5)(3), what is the value of a ?

Given Equation: We are given the equation 3^(a) = root(5)(3), which means that 3 raised to the power of a is equal to the fifth root of 3. To find the value of a, we need to express both sides of the equation in a way that allows us to compare the exponents directly.Rewriting Equation: The fifth root of 3 can be written as 3^(1/5). So, we can rewrite the equation as 3^(a) = 3^(1/5).Setting Exponents Equal: Since the bases are the same (both are 3), we can set the exponents equal to each other for the equation to hold true. Therefore, a must be equal to 1/5. a = 1/5Error Checking: We check for any mathematical errors in the previous steps. The steps followed the rules of exponents correctly, and there were no arithmetic errors.

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Factor sums and differences of cubes

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Q. If

3^{a}=\sqrt[5]{3}

, what is the value of

a

Given Equation: We are given the equation $3^{a} = \sqrt[5]{3}$ , which means that $3$ raised to the power of $a$ is equal to the fifth root of $3$ . To find the value of $a$ , we need to express both sides of the equation in a way that allows us to compare the exponents directly.
Rewriting Equation: The fifth root of $3$ can be written as $3^{(1/5)}$ . So, we can rewrite the equation as $3^{a} = 3^{(1/5)}$ .
Setting Exponents Equal: Since the bases are the same (both are $3$ ), we can set the exponents equal to each other for the equation to hold true. Therefore, $a$ must be equal to $\frac{1}{5}$ . $\newline$ $a = \frac{1}{5}$
Error Checking: We check for any mathematical errors in the previous steps. The steps followed the rules of exponents correctly, and there were no arithmetic errors.