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You are given a rectangle with base 3x^5y^4 and height (5x^3y^2). What expression that would represent the area of the rectangle?

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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.

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