Evaluate the following to determine the value of 𝑛: (8^3)^n = 8^12 (2 points) Responses n = 9 n = 9 n = 4 n = 4 n = 2 n = 2 n = 1

Answer 1

To solve the equation \((8^3)^n = 8^{12}\), we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\).

So we can rewrite the left side:

\[ (8^3)^n = 8^{3n} \]

Now the equation becomes:

\[ 8^{3n} = 8^{12} \]

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

\[ 3n = 12 \]

Next, we can solve for \(n\) by dividing both sides by 3:

\[ n = \frac{12}{3} = 4 \]

Thus, the value of \(n\) is \(4\).

The correct value of \(n\) is: n = 4.