Question

What is the value of n in the numerical sentence below?

The square root of 16 divided by 4^3 = 4^n

Answer 1

Use explanation in picture

Answer 2

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