Answer :
Let's go through each expression to determine which ones 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 check each of the given expressions:
a. 7:
- The expression 7 is just the number 7, which is not equal to 81.
b. [tex]\(4^3\)[/tex]:
- [tex]\(4^3 = 4 \times 4 \times 4 = 64\)[/tex], which is not equal to 81.
c. 12:
- The expression 12 is just the number 12, which is not equal to 81.
d. 81:
- The expression is exactly 81, which is equal to 81.
e. 64:
- The expression 64 is the number 64, which is not equal to 81.
f. [tex]\(9^2 = 9 \times 9 = 81\)[/tex]:
- [tex]\(9^2 = 81\)[/tex], which is equal to 81.
So, the expressions that equal [tex]\(3^4\)[/tex] are [tex]\(81\)[/tex] and [tex]\(9^2 = 81\)[/tex]. These are option d and option f.
1. Calculate [tex]\(3^4\)[/tex]:
[tex]\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\][/tex]
Now, let's check each of the given expressions:
a. 7:
- The expression 7 is just the number 7, which is not equal to 81.
b. [tex]\(4^3\)[/tex]:
- [tex]\(4^3 = 4 \times 4 \times 4 = 64\)[/tex], which is not equal to 81.
c. 12:
- The expression 12 is just the number 12, which is not equal to 81.
d. 81:
- The expression is exactly 81, which is equal to 81.
e. 64:
- The expression 64 is the number 64, which is not equal to 81.
f. [tex]\(9^2 = 9 \times 9 = 81\)[/tex]:
- [tex]\(9^2 = 81\)[/tex], which is equal to 81.
So, the expressions that equal [tex]\(3^4\)[/tex] are [tex]\(81\)[/tex] and [tex]\(9^2 = 81\)[/tex]. These are option d and option f.
