Question
Rewrite \( \frac{1}{\sqrt[4]{y}} \) using rational exponents.
Ask by Vaughan Hilton. in Kenya
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \frac{1}{\sqrt[4]{y}} \) can be written as \( \frac{\sqrt[4]{y^3}}{y} \).
Solution
Calculate or simplify the expression \( 1/(y^(1/4)) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{1}{\left(y^{\frac{1}{4}}\right)}\)
- step1: Rewrite the expression:
\(\frac{1}{y^{\frac{1}{4}}}\)
- step2: Simplify:
\(\frac{1}{\sqrt[4]{y}}\)
- step3: Calculate:
\(\frac{\sqrt[4]{y^{3}}}{y}\)
The expression \( \frac{1}{\sqrt[4]{y}} \) can be rewritten using rational exponents as \( \frac{\sqrt[4]{y^3}}{y} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To rewrite \( \frac{1}{\sqrt[4]{y}} \) using rational exponents, we can express the fourth root as an exponent of \( y \). The fourth root of \( y \) is the same as \( y^{1/4} \). Therefore, we can rewrite the expression as: \[ \frac{1}{\sqrt[4]{y}} = y^{-1/4} \] So, \( \frac{1}{\sqrt[4]{y}} \) can be expressed using rational exponents as \( y^{-1/4} \).
