What exponent would make the two expressions equivalent: (16 x) 6=(16 18)

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User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
4 hours ago

To find the exponent that makes the two expressions equivalent, we start with the given expressions:

\[ (16^x)^6 = 16^{18} \]

Using the property of exponents that states \((a^m)^n = a^{m \cdot n}\), we can simplify the left side of the equation:

\[ 16^{6x} = 16^{18} \]

Since the bases on both sides are the same (16), we can set the exponents equal to each other:

\[ 6x = 18 \]

Now, we solve for \(x\) by dividing both sides by 6:

\[ x = \frac{18}{6} = 3 \]

Thus, the exponent that makes the two expressions equivalent is

\[ \boxed{3}. \]