In the following equation, what is the value of n?
8^n = 8^-3 · 8^7
n =
In the following equation, what is the value of n?
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In the following equation, what is the value of n?
8^n = 8^-3 · 8^7
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 ).