In the following equation, what is the value of n?

To solve the equation ( 8^n = 8^{-3} cdot 8^7 ), we can use the property of exponents that states ( a^m cdot a^n = a^{m+n} ).

1. Combine the exponents on the right side:

[

8^{-3} cdot 8^7 = 8^{-3 + 7} = 8^4

]

2. Now we have:

[

8^n = 8^4

]

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

[

n = 4

]

So, the value of ( n ) is ( 4 ).