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The length and breadth of a room are 3x^(2)y^(3) and 6x^(3)y^(2). Find its and area.

66. The length and breadth of a room are 3x2y3 3 x^{2} y^{3} and 6x3y2 6 x^{3} y^{2} . Find its and area.

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Q. 66. The length and breadth of a room are 3x2y3 3 x^{2} y^{3} and 6x3y2 6 x^{3} y^{2} . Find its and area.
  1. Multiply Length and Breadth: To find the area of a rectangle, we multiply the length by the breadth.\newlineArea = Length×Breadth\text{Length} \times \text{Breadth}
  2. Substitute Given Expressions: Substitute the given expressions for length and breadth into the area formula.\newlineArea = (3x2y3)×(6x3y2)(3x^{2}y^{3}) \times (6x^{3}y^{2})
  3. Multiply Coefficients and Variables: Multiply the coefficients (numerical parts) and the variables separately, using the properties of exponents.\newlineArea = 3×6×x(2+3)×y(3+2)3 \times 6 \times x^{(2+3)} \times y^{(3+2)}
  4. Perform Final Calculation: Perform the multiplication of the coefficients and add the exponents for the variables with the same base.\newlineArea = 18x5y518x^{5}y^{5}

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