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Simplify the following. a) ((y⁻³ x y2) / y⁻⁷)1/2

Mathematics

ScanSolve AI Answer

Answer

y3y^3

Step-by-step solution

3 steps

  1. Simplify the numerator using the rule am×an=am+na^m \times a^n = a^{m+n}.

    y−3×y2=y−3+2=y−1y^{-3} \times y^2 = y^{-3+2} = y^{-1}

  2. Simplify the fraction using the rule aman=am−n\frac{a^m}{a^n} = a^{m-n}.

    y−1y−7=y−1−(−7)=y−1+7=y6\frac{y^{-1}}{y^{-7}} = y^{-1 - (-7)} = y^{-1+7} = y^6

  3. Apply the outer exponent using the rule (am)n=am×n(a^m)^n = a^{m \times n}.

    (y6)12=y6×12=y3(y^6)^{\frac{1}{2}} = y^{6 \times \frac{1}{2}} = y^3

    The simplified expression is:

    y3y^3
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