What is the value of n in the numerical sentence below? The square root of 16 divided by 4³ = 4ⁿ

Solution:

It is given that

square root of 16 divided by 4³ = 4ⁿ

We can write it as

√16/ 4³ = 4ⁿ

By cross multiplication

√16 = 4ⁿ × 4³

By applying the product rule :

a^m× aⁿ = a^{m + n}

4 = 4^{3 + n}

By applying the exponential rule :

x^m= xⁿ, m = n

1 = 3 + n

n = 1 - 3

n = -2

Therefore, the value of n is -2.

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What is the value of n in the numerical sentence below? The square root of 16 divided by 4³ = 4ⁿ

Summary:

The value of n in the numerical sentence the square root of 16 divided by 4³ = 4ⁿ is -2.