Which expression describes the area in square units of a
rectangle that has a width of 4x3y
2
and a length of 3x2y
3
?
At least try to write the question properly.
If your expression means:
W = 4 x³ y²
L = 3 x² y³
then
A = W ∙ L
A = 4 x³ y² ∙ 3 x² y³
A = 4 ∙ 3 ∙ x³ ⁺ ² ∙ y² ⁺ ³
A = 12 x⁵ y⁵
A = 12 ( x y )⁵
no idea what that all means; your text formatting is horrible.
But, if you mean the dimensions are
4x^3y^2 and 3x^2y^3
then the area is 4*3 x^(3+2) y^(2+3) = 12 x^5 y^5
if this exercise is just on learning rules of exponents, remember
x^a * x^b = x^(a+b)
when you multiply powers, you add exponents
To find the area of a rectangle, you multiply its length by its width. In this case, the width of the rectangle is 4x^3y^2 and the length is 3x^2y^3.
To multiply the two expressions, you multiply the coefficients together (4 * 3 = 12) and then multiply the variables with the same base (x^3 * x^2 = x^(3+2) = x^5 and y^2 * y^3 = y^(2+3) = y^5).
Therefore, the area of the rectangle can be represented as:
12x^5y^5 square units.