Question

2²⁰ + 2²⁰ = ______.

Options

• 2⁴⁰

• 2²¹

• 4²⁰

• 4⁴⁰

Answer 1

2²⁰ + 2²⁰ = 2²¹.

Explanation:

We are asked to simplify:

2²⁰ + 2²⁰

Step 1: Factor out the common term

Notice that both terms have the same base, 2²⁰.

So we can factor out 2²⁰ from both terms:

2²⁰ + 2²⁰ = 2²⁰(1 + 1)

Step 2: Simplify

1 + 1 = 2

So the expression becomes:

2²⁰ × 2 = 2²⁰ × 2¹

Step 3: Use the property of exponents

Use the property a^m × aⁿ = a^{m + n} to combine the exponents:

2²⁰ × 2¹ = 2^{20 + 1} = 2²¹

The value of 2²⁰ + 2²⁰ is 2²¹.