Question

radicals and rational exponents: foundations
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if $4^a = \sqrt6{4}$, what is the value of $a$?

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Explanation:

Step1: Rewrite the radical as an exponent

Recall that $\sqrt[n]{x}=x^{\frac{1}{n}}$. So, $\sqrt[6]{4}=4^{\frac{1}{6}}$.

Step2: Set the exponents equal

We have the equation $4^{a}=4^{\frac{1}{6}}$. Since the bases are the same and the exponential function is one - to - one (for $y = b^{x}$, when $b>0,b
eq1$, if $b^{m}=b^{n}$, then $m = n$), we can set the exponents equal to each other. So, $a=\frac{1}{6}$.

Answer:

$\frac{1}{6}$