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Answer :
To find the width of the table top, we can use the formula for the area of a rectangle, which is:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
In this problem, we are given:
- The area of the table top is [tex]\( 3^7 \)[/tex] square inches.
- The length of the table top is [tex]\( 3^4 \)[/tex] inches.
We need to find the width. We can rearrange the formula to solve for width:
[tex]\[ \text{Width} = \frac{\text{Area}}{\text{Length}} \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{Width} = \frac{3^7}{3^4} \][/tex]
When you divide powers with the same base, you subtract the exponents:
[tex]\[ \text{Width} = 3^{7-4} \][/tex]
[tex]\[ \text{Width} = 3^3 \][/tex]
Calculate [tex]\( 3^3 \)[/tex]:
[tex]\[ 3^3 = 27 \][/tex]
So, the width of the table top is 27 inches.
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
In this problem, we are given:
- The area of the table top is [tex]\( 3^7 \)[/tex] square inches.
- The length of the table top is [tex]\( 3^4 \)[/tex] inches.
We need to find the width. We can rearrange the formula to solve for width:
[tex]\[ \text{Width} = \frac{\text{Area}}{\text{Length}} \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{Width} = \frac{3^7}{3^4} \][/tex]
When you divide powers with the same base, you subtract the exponents:
[tex]\[ \text{Width} = 3^{7-4} \][/tex]
[tex]\[ \text{Width} = 3^3 \][/tex]
Calculate [tex]\( 3^3 \)[/tex]:
[tex]\[ 3^3 = 27 \][/tex]
So, the width of the table top is 27 inches.
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