Question

Evaluate 2 power 38 +2 power 37+2 power power 36 by 2 power 39+2power38+2power37

Answer 1

after simplify the answer is 1/2

Answer 2

(2³⁸ + 2³⁷ + 2³⁶)/(2³⁹ + 2³⁸ + 2³⁷) = 1/2

Step-by-step explanation:

∴ (2³⁸ + 2³⁷ + 2³⁶)/(2³⁹ + 2³⁸ + 2³⁷)

= (2³⁸ + 2³⁷ + 2³⁶)/(2³⁸⁺¹ + 2³⁷⁺¹ + 2³⁶⁺¹)

= (2³⁸ + 2³⁷ + 2³⁶)/(2³⁸ * 2 + 2³⁷ * 2 + 2³⁶ * 2)

= (2³⁸ + 2³⁷ + 2³⁶)/{2 * (2³⁸ + 2³⁷ + 2³⁶)}

= 1/2

Laws of indices:

• aᶜ * bᶜ = (ab)ᶜ

• aᵇ⁺ᶜ = aᵇ * aᶜ

• a⁻ᵇ = 1/aᵇ

Note: To solve this type of problems, always remember to find if there is any term common in both the numerator and the denominator. Then use the laws of indices. You will find a simplified form.