Question
Which expression is equivalent to \( 5 y^{-3} \) ? \( \frac{1}{125 y^{3}} \) \( \frac{1}{5 y^{3}} \) \( \frac{5}{y^{3}} \) \( \frac{125}{y^{3}} \)
Ask by Davison Nunez. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equivalent expression is \( \frac{5}{y^{3}} \).
Solution
To simplify 5y⁻³, recall that a negative exponent indicates the reciprocal. Thus, y⁻³ is equivalent to 1/y³, and the expression becomes:
5 * (1/y³) = 5/y³.
So, the equivalent expression is 5/y³.
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Simplify this solution Bonus Knowledge
To find an equivalent expression for \( 5 y^{-3} \), we can use the property of negative exponents that states \( a^{-n} = \frac{1}{a^n} \). So, \( y^{-3} \) can be rewritten as \( \frac{1}{y^3} \). Thus, \( 5 y^{-3} \) becomes \( 5 \cdot \frac{1}{y^3} = \frac{5}{y^3} \). This means the equivalent expression is \( \frac{5}{y^{3}} \).
