If 7^(a)=root(3)(7), what is the value of a ?

Given Equation: We are given the equation 7^(a) = root(3)(7). The cube root of 7 can be written as 7^(1/3).Equating Exponents: Now we have 7^(a) = 7^(1/3). Since the bases are the same, we can equate the exponents.Final Result: Setting the exponents equal to each other gives us a = 1/3.

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If
7^(a)=root(3)(7), what is the value of
a ?

If $7^{a}=\sqrt[3]{7}$ , 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[3]{7}

, what is the value of

a

Given Equation: We are given the equation $7^{a} = \sqrt[3]{7}$ . The cube root of $7$ can be written as $7^{\frac{1}{3}}$ .
Equating Exponents: Now we have $7^{a} = 7^{\frac{1}{3}}$ . Since the bases are the same, we can equate the exponents.
Final Result: Setting the exponents equal to each other gives us $a = \frac{1}{3}$ .