Question

2²⁰ + 16⁵ = ______.

Options

• 2⁴⁰

• 2²¹

• 2²⁵

• 2²⁰

Answer 1

2²⁰ + 16⁵ = 2²¹.

Explanation:

We are given the expression:

2²⁰ + 16⁵

Step 1: Rewrite 16 as a power of 2

We know that:

16 = 2⁴

So, we can rewrite 16⁵ as:

16⁵ = (2⁴)⁵ = 2²⁰

Step 2: Substitute and simplify

Now the expression becomes:

2²⁰ + 2²⁰

Step 3: Combine the terms

Since both terms are 2²⁰, we can factor them:

2²⁰ + 2²⁰  = 2 × 2²⁰

= 2^{1 + 20} 

= 2²¹

Thus, the value of the expression is 2²¹