What exponent would make the two expressions equivalent (3³)^=3²⁴?
A. 21
B. 8
C. 15
D. 27
To make the two expressions equivalent, we need to find an exponent that will result in the same value for both expressions.
The value of the expression (3³) is equal to 3 raised to the power of 3, which is equal to 3 * 3 * 3 = 27.
The value of the expression 3²⁴ is equal to 3 raised to the power of 24, which is equal to 3 * 3 * 3 * ... * 3 (24 times).
So we need to find an exponent that will result in 27 when raised to that power. Looking at the answer choices, we see that D. 27 is the only option that matches this requirement.
Therefore, the exponent that would make the two expressions equivalent is:
D. 27
To make the two expressions equivalent, we need to find the exponent that would make (3³) equal to 3²⁴.
The exponent in the expression (3³) is 3, which means we multiply 3 three times.
So, (3³) can be simplified to 3 * 3 * 3 = 27.
Now we can compare 27 to 3²⁴.
Since 27 is not equal to 3²⁴, we need to find the exponent that would make them equal.
Let's check the given options:
A. 21: 3²¹ = 9,536,743,164,062,500
B. 8: 3⁸ = 6,561
C. 15: 3¹⁵ = 14,348,907
D. 27: 3²⁷ = 762,559,748,498,676,640,000
None of the given options makes the two expressions equivalent.
Therefore, there is no exponent that would make (3³) equal to 3²⁴.