If 5^(a)=root(3)(5^(2)), what is the value of a ?

Given Equation Analysis: We are given the equation 5^(a) = root(3)(5^(2)). To solve for a, we need to express both sides of the equation with the same base and then compare the exponents.Cube Root Property: The cube root of a number is the same as raising that number to the power of 1/3. Therefore, we can rewrite the equation as 5^(a) = (5^(2))^(1/3).Simplify Exponents: Using the property of exponents that (x^(m))^(n) = x^(m*n), we can simplify the right side of the equation to 5^(2/3). 5^(a) = 5^(2/3)Set Exponents Equal: Since the bases are the same (5), we can set the exponents equal to each other. This gives us the equation a = 2/3.Final Answer: We have found the value of a to be 2/3, which is the final answer.

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Algebra 2

Factor sums and differences of cubes

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Q. If

5^{a}=\sqrt[3]{5^{2}}

, what is the value of

a

Given Equation Analysis: We are given the equation $5^{a} = \sqrt[3]{5^{2}}$ . To solve for $a$ , we need to express both sides of the equation with the same base and then compare the exponents.
Cube Root Property: The cube root of a number is the same as raising that number to the power of $\frac{1}{3}$ . Therefore, we can rewrite the equation as $5^{a} = (5^{2})^{\frac{1}{3}}$ .
Simplify Exponents: Using the property of exponents that $(x^{m})^{n} = x^{m*n}$ , we can simplify the right side of the equation to $5^{\frac{2}{3}}$ . $\newline$ $5^{a} = 5^{\frac{2}{3}}$
Set Exponents Equal: Since the bases are the same $5$ , we can set the exponents equal to each other. This gives us the equation $a = \frac{2}{3}$ .
Final Answer: We have found the value of $a$ to be $\frac{2}{3}$ , which is the final answer.