Which expression describes the area in square units of the rectangle that has a length of 10x^3y^4 units and a width of 5x^2y units?
area = length * width
= 10x^3y^4 * 5x^2y
= 10*5 x^(3+2) y^(4+1)
= 50 x^5 y^5
To find the area of a rectangle, we multiply its length by its width.
In this case, the length of the rectangle is given as 10x^3y^4 units, and the width is given as 5x^2y units.
To multiply terms with the same base, we add their exponents. So, to find the area, we need to multiply the coefficients (numbers in front of the variables) and add the exponents of each variable.
The coefficients are 10 and 5.
The variable x has an exponent of 3 in the length and an exponent of 2 in the width, so we add 3 and 2 to get 5.
The variable y has an exponent of 4 in the length and an exponent of 1 in the width, so we add 4 and 1 to get 5.
Putting it all together, the expression that describes the area of the rectangle is:
10x^3y^4 * 5x^2y = 50x^(3+2)y^(4+1) = 50x^5y^5.
So, the area of the rectangle is 50x^5y^5 square units.