To determine the correct expression for the total volume of all the pans, we need to follow these steps:
1. Calculate the volume of one baking pan:
- Each pan is 7 inches in length, 7 inches in width, and 2 inches in height.
- The volume [tex]\( V \)[/tex] of a rectangular or square prism is given by the formula: [tex]\( V = \text{length} \times \text{width} \times \text{height} \)[/tex].
- For one pan: [tex]\( V = 7 \times 7 \times 2 \)[/tex].
2. Simplify the expression for one pan's volume:
- [tex]\( 7 \times 7 \times 2 = 49 \times 2 = 98 \)[/tex] cubic inches.
3. Calculate the total volume for all 4 pans:
- Frances has 4 such pans, so to find the total volume, we multiply the volume of one pan by 4.
- Total volume = [tex]\( 98 \times 4 \)[/tex].
4. Put it all together:
- Let's analyze each option:
A. [tex]\( 7^{\wedge} 2 \times 2 \)[/tex] translates to [tex]\( 7^2 \times 2 \)[/tex] which is [tex]\( 49 \times 2 = 98 \)[/tex]. This is the volume of one pan, not the total volume of all four pans.
B. [tex]\( 7 \times 2^{\wedge} 4 \)[/tex] translates to [tex]\( 7 \times 2^4 \)[/tex] which is [tex]\( 7 \times 16 = 112 \)[/tex]. This is incorrect.
C. [tex]\( (7 \times 2 \times 2) \times 4 \)[/tex] translates to [tex]\( 7 \times 2 = 14 \)[/tex], so [tex]\( 14 \times 2 = 28 \)[/tex]. Then [tex]\( 28 \times 4 = 112 \)[/tex]. This is incorrect.
D. [tex]\( \left(7^{\wedge} 2 \times 2\right) \times 4 \)[/tex] translates to [tex]\( 7^2 \times 2 \)[/tex], which is [tex]\( 49 \times 2 = 98 \)[/tex]. Then [tex]\( 98 \times 4 = 392 \)[/tex]. This is correct.
So, the correct expression that gives the total volume of all the pans is:
D. [tex]\( \left(7^{\wedge} 2 \times 2\right) \times 4 \)[/tex]
