Answer:
The value of n=-2
Step-by-step explanation:
Given : The square root of 16 divided by \(4^3 = 4^n\)
To find : The value of n
Solution :
According to given statement,
The square root of 16 divided by \(4^3 = 4^n\)
\(\frac{\sqrt{16}}{4^3}=4^n\)
\(\sqrt{16}=4^n\times 4^3\)
Applying product rule when bases are same power is added
\(x^m \cdot x^n= x^{m+n}\)
\(4=4^{3+n}\)
According to exponential rule,
If \(x^m=x^n\Rightarrow m=n\)
So, \(1=3+n\)
\(n=-2\)
Therefore, The value of n is -2
