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Select all the expressions that equal [tex]$3^4$[/tex].

A. 7
B. [tex]$4^3$[/tex]
C. 12
D. 81
E. 64
F. [tex]$9^2 = 9 \times 9 = 81$[/tex]

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.

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