To determine which expression has a value of 3, let's evaluate each of the given expressions step by step:
#### Expression (a):
[tex]\[ 3 \left( 4^2 - 3^2 \right) \][/tex]
1. Calculate [tex]\(4^2\)[/tex]:
[tex]\[ 4^2 = 16 \][/tex]
2. Calculate [tex]\(3^2\)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]
3. Compute the difference:
[tex]\[ 16 - 9 = 7 \][/tex]
4. Multiply by 3:
[tex]\[ 3 \cdot 7 = 21 \][/tex]
So, the value of expression (a) is 21.
#### Expression (b):
[tex]\[ 24 - 23 \cdot 3 \][/tex]
1. Calculate [tex]\(23 \cdot 3\)[/tex]:
[tex]\[ 23 \cdot 3 = 69 \][/tex]
2. Subtract from 24:
[tex]\[ 24 - 69 = -45 \][/tex]
So, the value of expression (b) is -45.
#### Expression (c):
[tex]\[ 3^3 - 3^2 \][/tex]
1. Calculate [tex]\(3^3\)[/tex]:
[tex]\[ 3^3 = 27 \][/tex]
2. Calculate [tex]\(3^2\)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]
3. Subtract the second result from the first:
[tex]\[ 27 - 9 = 18 \][/tex]
So, the value of expression (c) is 18.
#### Expression (d):
[tex]\[ \left(6^2 - 3\right) \left( 9^2 - 70 \) \][/tex]
1. Calculate [tex]\(6^2\)[/tex]:
[tex]\[ 6^2 = 36 \][/tex]
2. Subtract 3 from 36:
[tex]\[ 36 - 3 = 33 \][/tex]
3. Calculate [tex]\(9^2\)[/tex]:
[tex]\[ 9^2 = 81 \][/tex]
4. Subtract 70 from 81:
[tex]\[ 81 - 70 = 11 \][/tex]
5. Multiply the results:
[tex]\[ 33 \cdot 11 = 363 \][/tex]
So, the value of expression (d) is 363.
### Summary
- Expression (a) has a value of [tex]\( 21 \)[/tex]
- Expression (b) has a value of [tex]\( -45 \)[/tex]
- Expression (c) has a value of [tex]\( 18 \)[/tex]
- Expression (d) has a value of [tex]\( 363 \)[/tex]
None of these expressions equal 3. Therefore, the correct answer is:
None of the expressions has a value of 3.
