If 7^(a)=root(8)(7), what is the value of a ?

Given Equation: We are given that 7^(a) = root(8)(7), which means that 7 is raised to the power of a and this is equal to the eighth root of 7. The eighth root of a number is the same as raising that number to the power of 1/8. So we can rewrite the equation as: 7^(a) = 7^(1/8)Equating Exponents: Since the bases are the same (both are 7), we can equate the exponents. This gives us: a = 1/8Finding the Value of a: We have found the value of a without any need for further simplification or calculation. There is no math error in this step.

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If
7^(a)=root(8)(7), what is the value of
a ?

If $7^{a}=\sqrt[8]{7}$ , what is the value of $a$ ?

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Math Problems

Algebra 2

Factor sums and differences of cubes

Full solution

Q. If

7^{a}=\sqrt[8]{7}

, what is the value of

a

Given Equation: We are given the equation $7^{a} = \sqrt[8]{7}$ . 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 eighth root of a number is the same as raising that number to the power of $\frac{1}{8}$ . Therefore, we can rewrite the equation as $7^{a} = 7^{\frac{1}{8}}$ .
Equate Exponents: Now we have $7^{a} = 7^{\frac{1}{8}}$ . Since the bases are the same, we can equate the exponents: $\newline$ $a = \frac{1}{8}$
Final Answer: We have found the value of $a$ to be $\frac{1}{8}$ , which is the final answer.