Question

the rectangle to the right has width $2x^4$ feet and length $8x^5$ feet. find its area as an expression of $x$.
the area of the rectangle is \square square feet.
(simplify your answer)

Explanation:

Step1: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by the product of its length \( l \) and width \( w \), so \( A = l \times w \).

Step2: Substitute the given length and width

Here, the length \( l = 8x^5 \) feet and the width \( w = 2x^4 \) feet. Substituting these into the formula, we get \( A=(8x^5)\times(2x^4) \).

Step3: Multiply the coefficients and use the exponent rule for multiplication

First, multiply the coefficients: \( 8\times2 = 16 \). Then, use the rule of exponents \( a^m\times a^n=a^{m + n} \) for the variable \( x \): \( x^5\times x^4=x^{5 + 4}=x^9 \). Combining these results, we have \( A = 16x^9 \).

Answer:

\( 16x^9 \)