Reeves Coles
09/22/2023 · Middle School
What exponent would make the two expressions equivalent: \( \left(3^{3}\right)^{x}=3^{24} \) ? (1 point) 8 21 27 15
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the equation \( \left(3^{3}\right)^{x}=3^{24} \), we can use the property of exponents that states \( (a^m)^n = a^{m \cdot n} \).
Applying this property, we have:
\[
\left(3^{3}\right)^{x} = 3^{3x}
\]
Now, we can rewrite the equation as:
\[
3^{3x} = 3^{24}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
3x = 24
\]
To solve for \( x \), divide both sides by 3:
\[
x = \frac{24}{3} = 8
\]
Thus, the exponent that makes the two expressions equivalent is:
\[
\boxed{8}
\]
Quick Answer
The exponent is 8.
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