If 11^(a)=root(7)(11), what is the value of a ?

Given equation: We are given the equation 11^(a) = root(7)(11). The right side of the equation is the 7th root of 11, which can be written as 11^(1/7).Equating the exponents: Now we have 11^(a) = 11^(1/7). Since the bases are the same, we can equate the exponents. This gives us a = 1/7.Checking for errors: We check for any mathematical errors. The steps followed the rules of exponents correctly, and there are no arithmetic errors.

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If
11^(a)=root(7)(11), what is the value of
a ?

If $11^{a}=\sqrt[7]{11}$ , what is the value of $a$ ?

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Math Problems

Algebra 2

Factor sums and differences of cubes

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Q. If

11^{a}=\sqrt[7]{11}

, what is the value of

a

Given Equation: We are given the equation $11^{a} = \sqrt[7]{11}$ . To solve for $a$ , we need to express both sides of the equation with the same base and exponent format.
Express with Same Base: The seventh root of a number is the same as raising that number to the power of $\frac{1}{7}$ . Therefore, we can rewrite the equation as $11^{a} = 11^{\frac{1}{7}}$ .
Equate Exponents: Now we have $11^{a} = 11^{\frac{1}{7}}$ . Since the bases are the same, we can equate the exponents: $\newline$ $a = \frac{1}{7}$
Final Answer: We have found the value of $a$ to be $\frac{1}{7}$ , which is the final answer.