Evaluate the following to determine the value of 𝑛:

Question

(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 $(a^m{)}^n=a^{m\cdot n}$.

Applying this property, we have:

$$(8^3{)}^n=8^{3n}$$

Thus, we can rewrite the equation as:

$$8^{3n}=8^{12}$$

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

$$3n=12$$

Now, we solve for $n$:

$$n=\frac{12}{3}=4$$

Therefore, the value of $n$ is:

$$\boxed{{\displaystyle 4}}$$