Final answer:
The area of a rectangle with base 3x^5y^4 and height 5x^3y^2 is 15x^8y^6, found by multiplying the base and height and applying the properties of exponents.
Step-by-step explanation:
To find the area of a rectangle, you multiply the base by the height. Given the base as 3x^5y^4 and the height as (5x^3y^2), the area can be calculated as follows:
Area = Base × Height
Area = (3x^5y^4) × (5x^3y^2)
To multiply these expressions, you multiply the coefficients (numerical parts) and add the exponents for the like variables according to the properties of exponents.
Therefore, Area = 3 × 5 × x^(5+3) × y^(4+2)
Area = 15x^8y^6
This is the expression that represents the area of the rectangle. Here, we have combined like terms and applied the correct properties of exponents.