Question

what exponent would make (16^x)^6 = (16^18) equivalent

Answer 1

To solve the equation \((16^x)^6 = (16^{18})\), we can first simplify both sides.

Using the rule of exponents \((a^m)^n = a^{m \cdot n}\), we can rewrite the left side:

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

Now, we can set the equation:

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

Since the bases are the same, we can equate the exponents:

\[
6x = 18
\]

Now, solve for \(x\):

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

Thus, the exponent \(x\) that would make \((16^x)^6 = (16^{18})\) equivalent is

\[
\boxed{3}
\]