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

Question

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Answer 1

To solve the equation \((16^x)^6 = 16^{18}\), we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\).

Applying this property to the left side of the equation, we get:

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

So 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:

\[ 6x = 18 \]

Now, 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:

\[ \boxed{3} \]