Question

the rectangle to the right has width 3x^7 feet and length 9x^5 feet. find its area as an expression of x. the area of the rectangle is (simplify your answer.)

Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = l\times w$, where $l$ is length and $w$ is width.

Step2: Substitute given values

Here, $l = 9x^{5}$ and $w=3x^{7}$. So $A=(9x^{5})\times(3x^{7})$.

Step3: Multiply coefficients and add exponents

Multiply the coefficients $9\times3 = 27$, and add the exponents of $x$ using the rule $a^{m}\times a^{n}=a^{m + n}$, so $x^{5}\times x^{7}=x^{5 + 7}=x^{12}$. Then $A = 27x^{12}$.

Answer:

$27x^{12}$