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

1 answer

To solve the equation \((8^3)^n = 8^{12}\), we can start by simplifying the left side:

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

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

So, we can rewrite the equation as:

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

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

\[ 3n = 12 \]

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

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

Thus, the value of \(n\) is:

\[ \boxed{4} \]