Question

please answer this


find the value of n if 2^10=2^-2*2^3n

Answer 1

Answer:

n = 4

Step-by-step explanation:

Given: 2¹⁰ = 2⁻² * 2³ⁿ

Divide both sides by '2⁻²'

⇒ (2¹⁰/2⁻²) = (2⁻² * 2³ⁿ/2⁻²)

⇒ (2¹⁰/2⁻²) = 2³ⁿ

We know that (xᵃ/xᵇ) = (xᵃ⁻ᵇ)

⇒ 2¹⁰⁻⁽⁻²⁾ = 2³ⁿ

⇒ 2¹⁰⁺² = 2³ⁿ

⇒ 2¹² = 2³ⁿ

We know that aⁿ = aˣ, then n = x.

⇒ 12 = 3n

Divide both sides by '3', we get

⇒ (12/3) = (3n/3)

⇒ n = 4

Therefore, the value of n = 4.

Hope it helps!