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4. \( \left(\frac{5 x^{0}}{10 x^{-3} y^{2}}\right)^{2} \)

Ask by Knight Pollard. in the United States
Mar 11,2025

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The simplified expression is \( \frac{x^{6}}{4y^{4}} \).

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To simplify the expression \( \left(\frac{5 x^{0}}{10 x^{-3} y^{2}}\right)^{2} \), we can start by noting that \( x^{0} = 1 \). This simplifies the fraction to \( \frac{5}{10 x^{-3} y^{2}} \), which further reduces to \( \frac{1}{2 x^{-3} y^{2}} \). When we deal with negative exponents, remember that \( x^{-3} = \frac{1}{x^{3}} \), so we rewrite the expression as \( \frac{1}{2 \cdot \frac{1}{x^{3}} \cdot y^{2}} = \frac{x^{3}}{2y^{2}} \). Now, raising this to the power of 2 gives us: \[ \left(\frac{x^{3}}{2y^{2}}\right)^{2} = \frac{x^{6}}{4y^{4}}. \] So, the simplified expression is \( \frac{x^{6}}{4y^{4}} \). Now your expression is neat and tidy!

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