Question
Using the properties of exponents, which expression is equivalent to x/x3/4?(1 point) Responses 1x√4 Start Fraction 1 over root index 4 Start Root x End Root End Fraction x x x4 x superscript 4 baseline x−−√4
Answers
Answered by
GPT-4o mini
To simplify the expression \( \frac{x}{x^{3/4}} \) using the properties of exponents, we can apply the rule \( \frac{a^m}{a^n} = a^{m-n} \).
Thus, we have:
\[
\frac{x}{x^{3/4}} = x^{1 - \frac{3}{4}} = x^{\frac{4}{4} - \frac{3}{4}} = x^{\frac{1}{4}}
\]
The expression \( x^{\frac{1}{4}} \) can also be written as \( \sqrt[4]{x} \).
Therefore, the equivalent expression is \( \sqrt[4]{x} \).
Given your response options, the correct choice should be related to \( x^{1/4} \) or \( \sqrt[4]{x} \).
If the choices you provided include a choice representing \( \sqrt[4]{x} \), that would be the equivalent expression. If you meant any of the options written differently, please clarify, and I can assist accordingly.
Thus, we have:
\[
\frac{x}{x^{3/4}} = x^{1 - \frac{3}{4}} = x^{\frac{4}{4} - \frac{3}{4}} = x^{\frac{1}{4}}
\]
The expression \( x^{\frac{1}{4}} \) can also be written as \( \sqrt[4]{x} \).
Therefore, the equivalent expression is \( \sqrt[4]{x} \).
Given your response options, the correct choice should be related to \( x^{1/4} \) or \( \sqrt[4]{x} \).
If the choices you provided include a choice representing \( \sqrt[4]{x} \), that would be the equivalent expression. If you meant any of the options written differently, please clarify, and I can assist accordingly.
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