Question
Which expression is equivalent to \( \sqrt[4]{7} \) ? \( 4^{\frac{1}{7}} 4^{7} \) \( 7^{\frac{1}{4}} \) \( 7^{4} \)
Ask by Paul Carter. in the United States
Dec 12,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The expression equivalent to \( \sqrt[4]{7} \) is \( 7^{\frac{1}{4}} \).
Solution
To determine which expression is equivalent to \( \sqrt[4]{7} \), we can rewrite \( \sqrt[4]{7} \) in exponential form. The fourth root of a number can be expressed as that number raised to the power of \( \frac{1}{4} \):
\[
\sqrt[4]{7} = 7^{\frac{1}{4}}
\]
Now, let's analyze the options provided:
1. \( 4^{\frac{1}{7}} 4^{7} \): This expression does not simplify to \( \sqrt[4]{7} \).
2. \( 7^{\frac{1}{4}} \): This is exactly the same as \( \sqrt[4]{7} \).
3. \( 7^{4} \): This expression is not equivalent to \( \sqrt[4]{7} \).
Thus, the expression that is equivalent to \( \sqrt[4]{7} \) is:
\[
\boxed{7^{\frac{1}{4}}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find an expression equivalent to \( \sqrt[4]{7} \), recall that the fourth root of a number can be expressed as that number raised to the power of \( \frac{1}{4} \). Thus, \( \sqrt[4]{7} = 7^{\frac{1}{4}} \). Among the options provided, \( 7^{\frac{1}{4}} \) is indeed the correct equivalent expression. Also, it’s worth noting that many students stumble upon taking the root or fractional exponents. A common mistake is confusing the order of operations when solving problems involving roots, often leading to miscalculations. Always remember to convert roots to exponent form to clarify your calculations!
