Answer :
Sure! Let's solve the problem step-by-step.
We need to determine which expressions are equal to [tex]\(3^4\)[/tex].
1. Calculate [tex]\(3^4\)[/tex]:
[tex]\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\][/tex]
Now, let's evaluate each option to find which ones equal 81:
- Option A: 7
This is just a single number, and it is not equal to 81.
- Option B: [tex]\(4^3\)[/tex]
Calculate [tex]\(4^3\)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
This is not equal to 81.
- Option C: 12
This number is not equal to 81.
- Option D: 81
This number is exactly equal to 81.
- Option E: 64
This number is not equal to 81.
- Option F: [tex]\(9^2\)[/tex]
Calculate [tex]\(9^2\)[/tex]:
[tex]\[
9^2 = 9 \times 9 = 81
\][/tex]
This is equal to 81.
After checking all the options, the expressions that equal [tex]\(3^4\)[/tex] are:
- Option D: 81
- Option F: [tex]\(9^2\)[/tex]
These are the two expressions in the list that are equal to 81.
We need to determine which expressions are equal to [tex]\(3^4\)[/tex].
1. Calculate [tex]\(3^4\)[/tex]:
[tex]\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\][/tex]
Now, let's evaluate each option to find which ones equal 81:
- Option A: 7
This is just a single number, and it is not equal to 81.
- Option B: [tex]\(4^3\)[/tex]
Calculate [tex]\(4^3\)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
This is not equal to 81.
- Option C: 12
This number is not equal to 81.
- Option D: 81
This number is exactly equal to 81.
- Option E: 64
This number is not equal to 81.
- Option F: [tex]\(9^2\)[/tex]
Calculate [tex]\(9^2\)[/tex]:
[tex]\[
9^2 = 9 \times 9 = 81
\][/tex]
This is equal to 81.
After checking all the options, the expressions that equal [tex]\(3^4\)[/tex] are:
- Option D: 81
- Option F: [tex]\(9^2\)[/tex]
These are the two expressions in the list that are equal to 81.
