Question

the rectangle to the right has width 7x^4 feet and length 9x^3 feet. find its area as an expression of x. the area of the rectangle is
(simplify your answer.)

Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by the formula \( A=\text{length}\times\text{width} \). Here, the length is \( 9x^{3} \) feet and the width is \( 7x^{4} \) feet.

Step2: Multiply the coefficients and the variables

When multiplying monomials, we multiply the coefficients (the numerical parts) and add the exponents of the same base (using the rule \( a^{m}\times a^{n}=a^{m + n} \)).
First, multiply the coefficients: \( 9\times7 = 63 \).
Then, multiply the variables: \( x^{3}\times x^{4}=x^{3 + 4}=x^{7} \) (by the exponent rule for multiplication).
Combine these results: \( (9x^{3})\times(7x^{4})=9\times7\times x^{3}\times x^{4}=63x^{7} \).

Answer:

\( 63x^{7} \) square feet