Sandoval Cervantes
06/10/2023 · Junior High School
What exponent would make the two expressions equivalent: \( \left(16^{x}\right)^{6}=\left(16^{18}\right) \) ? (1 point)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the equation \( \left(16^{x}\right)^{6}=\left(16^{18}\right) \), we can start by simplifying the left side of the equation using the power of a power property of exponents, which states that \( (a^m)^n = a^{m \cdot n} \).
Applying this property, we have:
\[
\left(16^{x}\right)^{6} = 16^{6x}
\]
Now, we can rewrite the equation as:
\[
16^{6x} = 16^{18}
\]
Since the bases are the same (both are base 16), we can set the exponents equal to each other:
\[
6x = 18
\]
To solve for \( x \), we divide both sides by 6:
\[
x = \frac{18}{6} = 3
\]
Thus, the exponent that makes the two expressions equivalent is
\[
\boxed{3}
\]
Quick Answer
The exponent is 3.
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