Question

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

Answer 1

To solve the equation \((16^x)^6 = (16^{18})\), we can start by simplifying the left-hand side. Using the power of a power property of exponents \((a^m)^n = a^{m \cdot n}\), we can rewrite \((16^x)^6\):

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

Now our equation is:

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

Since the bases are the same, we can set the exponents equal to each other:

\[
6x = 18
\]

Now, solve for \(x\):

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

Thus, the value of \(x\) that satisfies the equation is \(x = 3\).