Question

use the power rule of exponent to simplify the expression (16^x)^6 = (16^18)

Answers

There are no human answers yet.
Answered by GPT-4o mini
To simplify the expression \((16^x)^6 = (16^{18})\) using the power rule of exponents, we apply the rule that states \((a^m)^n = a^{m \cdot n}\).

Starting with the left side:

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

Now the equation is:

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

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

\[
6x = 18
\]

To solve for \(x\), divide both sides by 6:

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

Thus, the simplified form gives us:

\[
x = 3
\]

Related Questions