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If
2^(a)=root(4)(2), what is the value of
a ?

If $2^{a}=\sqrt[4]{2}$ , what is the value of $a$ ?

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Solve equations using cube roots

Full solution

Q. If

2^{a}=\sqrt[4]{2}

, what is the value of

a

?

Given Equation: We are given the equation $2^{a} = \sqrt[4]{2}$ , which means that $2$ raised to the power of $a$ is equal to the fourth root of $2$ . The fourth root of a number is the same as raising that number to the power of $\frac{1}{4}$ . Therefore, we can rewrite the equation as: $\newline$ $2^{a} = 2^{\frac{1}{4}}$
Exponent Calculation: Since the bases on both sides of the equation are the same (base $2$ ), we can set the exponents equal to each other. This gives us: $\newline$ $a = \frac{1}{4}$
Final Result: We have found the value of $a$ to be $\frac{1}{4}$ , which is the exponent that makes $2^{a}$ equal to the fourth root of $2$ . There is no need for further calculation or simplification.

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