Answer :
To determine which expressions are equivalent to [tex]\(3^4\)[/tex], let's first identify the value of [tex]\(3^4\)[/tex]:
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \][/tex]
Now, let's evaluate each option to see if any match this value of 81:
- Option A: 7
7 is not equivalent to 81.
- Option B: [tex]\(4^3\)[/tex]
[tex]\[ 4^3 = 4 \times 4 \times 4 = 64 \][/tex]
64 is not equivalent to 81.
- Option C: 12
12 is not equivalent to 81.
- Option D: 81
This exactly matches the value of [tex]\(3^4\)[/tex], so it is equivalent.
- Option E: 64
64 is not equivalent to 81.
- Option F: [tex]\(9^2\)[/tex]
[tex]\[ 9^2 = 9 \times 9 = 81 \][/tex]
This matches the value of [tex]\(3^4\)[/tex], so it is also equivalent.
Therefore, the expressions that are equivalent to [tex]\(3^4\)[/tex] are:
- D. 81
- F. [tex]\(9^2\)[/tex]
These are the correct results, so options D and F are the ones equivalent to [tex]\(3^4\)[/tex].
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \][/tex]
Now, let's evaluate each option to see if any match this value of 81:
- Option A: 7
7 is not equivalent to 81.
- Option B: [tex]\(4^3\)[/tex]
[tex]\[ 4^3 = 4 \times 4 \times 4 = 64 \][/tex]
64 is not equivalent to 81.
- Option C: 12
12 is not equivalent to 81.
- Option D: 81
This exactly matches the value of [tex]\(3^4\)[/tex], so it is equivalent.
- Option E: 64
64 is not equivalent to 81.
- Option F: [tex]\(9^2\)[/tex]
[tex]\[ 9^2 = 9 \times 9 = 81 \][/tex]
This matches the value of [tex]\(3^4\)[/tex], so it is also equivalent.
Therefore, the expressions that are equivalent to [tex]\(3^4\)[/tex] are:
- D. 81
- F. [tex]\(9^2\)[/tex]
These are the correct results, so options D and F are the ones equivalent to [tex]\(3^4\)[/tex].
