Bot GPT 4-o mini To simplify the expression \( \frac{4 \sqrt{y^3}}{\sqrt{y^5}} \), we can follow these steps:
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Rewrite the square roots in terms of exponents. \[ \sqrt{y^3} = y^{3/2} \quad \text{and} \quad \sqrt{y^5} = y^{5/2} \]
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Substitute these back into the expression: \[ \frac{4 \cdot y^{3/2}}{y^{5/2}} \]
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Use the property of exponents to simplify: \[ \frac{y^{3/2}}{y^{5/2}} = y^{3/2 - 5/2} = y^{-2/2} = y^{-1} \]
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So, the expression becomes: \[ 4y^{-1} = \frac{4}{y} \]
Now, let's compare this to the provided options. The answer in simplified form is
\[ \frac{4}{y} = 4y^{-1} \]
None of the responses given match this simplified form directly, but the closest option is:
\[ 1/y^{7/4} \] If options were more likely to represent radical expressions, \( y^{-1} \) can typically represent a simplified form in many contexts, yet is still distinct from \( \frac{4}{y} \).
If there are more specific options or if I misunderstood the notation provided, please clarify! Based on this setup, none is equivalent to \( \frac{4}{y} \) among the given options completely.
1 answer