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

Given Equation: We are given the equation 2^(a) = root(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 1/4. Therefore, we can rewrite the equation as: 2^(a) = 2^(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: a = 1/4Final Result: We have found the value of a to be 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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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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Grade 8

Solve equations using cube roots

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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.