Question

Ellen’s dog has a pen that is 32 feet by 33 feet. What is the area of the dog pen?

A rectangle with length 3 cubed feet and width of 3 squared feet.

Find the area.

1. Multiply powers:    32 · 33

2. Expand each power:  (3 · 3) · (3 · 3 · 3)

3. Simplify:       35

 

Complete each sentence.

The
of the original exponent is the exponent in the power of product.
The dog pen has an area of
square feet.

Answer 1

To find the area of Ellen’s dog pen, which is a rectangle, you multiply the length and the width.

1. **Area Calculation for Dog Pen**:

Area = Length × Width

\[
\text{Area} = 32 \, \text{feet} \times 33 \, \text{feet}
\]

\[
\text{Area} = 1056 \, \text{square feet}
\]

So, The dog pen has an area of **1056 square feet**.

2. **Area Calculation for the Rectangle with Exponents**:

You provided a rectangle's dimensions in terms of exponents:

- Length: \(3^3\) feet
- Width: \(3^2\) feet

To find the area, multiply these powers:

\[
\text{Area} = 3^3 \times 3^2
\]

**Multiply powers**:

When multiplying powers with the same base, you add the exponents:

\[
\text{Area} = 3^{3 + 2} = 3^5
\]

Thus, the area in exponential form is \(3^5\).

3. **Complete the Sentences**:

- The **sum** of the original exponents is the exponent in the power of product.
- The dog pen has an area of **1056** square feet.

So, the final completed sentences are as follows:

- The **sum** of the original exponents is the exponent in the power of product.
- The dog pen has an area of **1056 square feet**.