Question

Evaluate: 2^38+2^37+2^36/2^39+2^38+2^37

Answer 1

Answer:

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

Step-by-step explanation:

Evaluate: 2^38+2^37+2^36/2^39+2^38+2^37

2³⁸ = 2³⁶⁺² = 2³⁶ * 2² = 4 * 2³⁶

2³⁷ = 2³⁶⁺¹ = 2³⁶ * 2¹ =  2 * 2³⁶

2³⁹ = 2³⁶⁺³ = 2³⁶ * 2³ = 8 * 2³⁶

Numerator = 2³⁸ + 2³⁷ + 2³⁶

=  4 * 2³⁶ + 2 * 2³⁶ + 2³⁶

Taking 2³⁶ common

= 2³⁶ ( 4 + 2 + 1)

= 2³⁶ * 7

Denominator = 2³⁹ + 2³⁸ + 2³⁷

= 8 * 2³⁶ + 4 * 2³⁶ + 2 * 2³⁶

= 2³⁶ ( 8 + 4 + 2)

= 2³⁶ * 14

Numerator/Denominator

= 2³⁶ * 7 / 2³⁶ * 14

= 7/14

= 1/2

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

Answer 2

Answer:

$\frac{1}{2}$

Step-by-step explanation:

$\frac{ {2}^{38} + {2}^{37} + {2}^{36} }{{2}^{39} + {2}^{38} + {2}^{37} } \\ \\ {2}^{38 - 39} + {2}^{37 - 38} + {2}^{36 - 37} \\ \\ {2}^{ - 1} + {2}^{ - 1} + {2}^{ - 1} \\ \\ \frac{1}{2} + \frac{1}{2} + \frac{1}{2} \\ \\ \frac{1 + 1 + 1}{2} \\ \\ \frac{1}{2}$

Hope this will help you !!