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Question 4 (1 point What is the simplified (16x^(5)y^(4))/(2y)*(xy^(2))/(2x^(3)y^(7))

Question 44 (11 point What is the simplified 16x5y42y⋅xy22x3y7 \frac{16 x^{5} y^{4}}{2 y} \cdot \frac{x y^{2}}{2 x^{3} y^{7}}

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Full solution

Q. Question 44 (11 point What is the simplified 16x5y42y⋅xy22x3y7 \frac{16 x^{5} y^{4}}{2 y} \cdot \frac{x y^{2}}{2 x^{3} y^{7}}
  1. Simplify Expression: First, let's simplify the expression by canceling out common factors in the numerator and denominator.\newline(16x5y4)/(2y)×(xy2)/(2x3y7)=(8x5y3)×(1/(2x2y5))(16x^{5}y^{4})/(2y) \times (xy^{2})/(2x^{3}y^{7}) = (8x^{5}y^{3}) \times (1/(2x^{2}y^{5}))
  2. Multiply Fractions: Now, multiply the two fractions together.\newline(8x5y3)×(12x2y5)=82×x5−2×y3−5(8x^{5}y^{3}) \times \left(\frac{1}{2x^{2}y^{5}}\right) = \frac{8}{2} \times x^{5-2} \times y^{3-5}
  3. Simplify Numbers and Exponents: Simplify the numbers and subtract the exponents. 4×x3×y−24 \times x^{3} \times y^{-2}
  4. Final Simplification: Since y−2y^{-2} is in the denominator, we can write it as 1/y21/y^{2}. 4x3y2\frac{4x^{3}}{y^{2}}

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