If 3^(a)=root(5)(3^(4)), what is the value of a ?

Given Information: We are given that 3^(a) is equal to the fifth root of 3^(4). The fifth root of a number is the same as raising that number to the power of 1/5. Therefore, we can rewrite the equation as: 3^(a) = (3^(4))^(1/5)Rewriting the Equation: Using the property of exponents that (x^(m))^(n) = x^(m*n), we can simplify the right side of the equation: 3^(a) = 3^(4 * 1/5)Simplifying the Equation: Now we have 3^(a) = 3^(4/5). Since the bases are the same and the equation states that the two expressions are equal, we can set the exponents equal to each other: a = 4/5Setting the Exponents Equal: We have found the value of a to be 4/5. There is no need for further calculation or simplification.

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Find derivatives using the chain rule II

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Q. If

3^{a}=\sqrt[5]{3^{4}}

, what is the value of

a

Given Information: We are given that $3^{a}$ is equal to the fifth root of $3^{4}$ . The fifth root of a number is the same as raising that number to the power of $\frac{1}{5}$ . Therefore, we can rewrite the equation as: $\newline$ $3^{a} = (3^{4})^{\frac{1}{5}}$
Rewriting the Equation: Using the property of exponents that $(x^{m})^{n} = x^{m*n}$ , we can simplify the right side of the equation: $\newline$ $3^{a} = 3^{4 \cdot \frac{1}{5}}$
Simplifying the Equation: Now we have $3^{a} = 3^{\frac{4}{5}}$ . Since the bases are the same and the equation states that the two expressions are equal, we can set the exponents equal to each other: $\newline$ $a = \frac{4}{5}$
Setting the Exponents Equal: We have found the value of $a$ to be $\frac{4}{5}$ . There is no need for further calculation or simplification.