If 4^(a)=root(6)(4), what is the value of a ?

Identify Equation: We are given the equation 4^(a) = root(6)(4). To find the value of a, we need to express both sides of the equation with the same base if possible.Express with Same Base: The sixth root of 4 can be written as 4^(1/6). So, we can rewrite the equation as 4^(a) = 4^(1/6).Set Exponents Equal: Since the bases are the same (4), we can set the exponents equal to each other. This gives us a = 1/6.Find Value of a: We have found the value of a without any need for further simplification. Therefore, a = 1/6.

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If
4^(a)=root(6)(4), what is the value of
a ?

If $4^{a}=\sqrt[6]{4}$ , what is the value of $a ?$

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Math Problems

Grade 8

Solve equations using cube roots

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Q. If

4^{a}=\sqrt[6]{4}

, what is the value of

a ?

Identify Equation: We are given the equation $4^{a} = \sqrt[6]{4}$ . To find the value of $a$ , we need to express both sides of the equation with the same base if possible.
Express with Same Base: The sixth root of $4$ can be written as $4^{\frac{1}{6}}$ . So, we can rewrite the equation as $4^{a} = 4^{\frac{1}{6}}$ .
Set Exponents Equal: Since the bases are the same $4$ , we can set the exponents equal to each other. This gives us $a = \frac{1}{6}$ .
Find Value of a: We have found the value of $a$ without any need for further simplification. Therefore, $a = \frac{1}{6}$ .