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

The value of n=-2

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`

`(√(16))/(4^3)=4^n`

`√(16)=4^n* 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