The length of a rectangle is represented by 36x^4y^3 and the width is 4xy. What is the area of x?

Question:

The length of a rectangle is represented by {eq}36x^4y^3 {/eq} and the width is {eq}4xy {/eq}. What is the area of {eq}x {/eq}?

Multiplying Monomials:

A monomial is a single term of a polynomial, so it is a single term that is a product of constants, variables, and/or positive integer powers of variables. We can multiply monomials by multiplying the constants by each other, and multiplying each common variable factor together using the rule of exponents that states {eq}a^{m}\cdot a^{n}=a^{m+n} {/eq}.

We are given that the length of our rectangle is 36x4y3, and the width is 4xy. The area of a rectangle is equal to its length times its width, so the area of this rectangle is equal to 36x4y3 times 4xy. Notice that both of these expressions are monomials, so we multiply them by multiplying the constants of each term and multiplying common variable factors of each term using our rule of exponents.

• {eq}\left ( 36x^{4}y^{3} \right )\left ( 4xy \right )=\left ( 36\cdot 4 \right )\left ( x^{4}\cdot x \right )\left ( y^{3} \cdot y\right )=144x^{4+1}y^{3+1}=144x^{5}y^{4} {/eq}

We get that the area of the rectangle is 144x5y4.