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Multiply. Simplify your answer.\newline15y2z15z×19y2z16z\frac{15y^2z}{15z} \times \frac{19y^2z}{16z}

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Q. Multiply. Simplify your answer.\newline15y2z15z×19y2z16z\frac{15y^2z}{15z} \times \frac{19y^2z}{16z}
  1. Write Problem, Identify Expressions: Write down the problem and identify the expressions to be multiplied.\newlineWe have the expression 15y2z15z×19y2z16z\frac{15y^2z}{15z} \times \frac{19y^2z}{16z}. We need to multiply the two fractions.
  2. Factor Out Common Terms: Factor out common terms in the numerators and denominators.\newlineIn the first fraction, 15y2z/15z15y^2z/15z, we can cancel out the common factor of 15z15z in the numerator and the denominator. In the second fraction, 19y2z/16z19y^2z/16z, we can cancel out the common factor of zz in the numerator and the denominator.
  3. Perform Cancellation: Perform the cancellation.\newlineAfter canceling out the common factors, the first fraction simplifies to y2y^2 and the second fraction simplifies to 19y216\frac{19y^2}{16}.
  4. Multiply Simplified Fractions: Multiply the simplified fractions.\newlineNow we multiply y2y^2 by 19y216\frac{19y^2}{16}. This gives us (y219y216)\left(\frac{y^2 \cdot 19y^2}{16}\right).
  5. Combine Like Terms: Combine like terms in the numerator.\newlineWhen we multiply y2y^2 by 19y219y^2, we add the exponents of yy because they have the same base. This gives us 19y(2+2)16\frac{19y^{(2+2)}}{16}, which simplifies to 19y416\frac{19y^4}{16}.
  6. Check for Further Simplification: Check if the expression can be simplified further. The expression 19y416\frac{19y^4}{16} cannot be simplified further because 1919 and 1616 have no common factors other than 11, and the variable yy is already in its simplest form.

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