2 to the power of 9 is?
The Correct Answer and Explanation is:
The value of 2 raised to the power of 9 (2^9) is 512.
Explanation:
The expression 2^9 means that you multiply the number 2 by itself 9 times. This is an example of exponential notation, where the base is 2 and the exponent (also called the power) is 9. To break it down:
2^9 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Now, let’s compute this step by step:
- 2^1 = 2
- 2^2 = 2 × 2 = 4
- 2^3 = 2 × 2 × 2 = 8
- 2^4 = 2 × 2 × 2 × 2 = 16
- 2^5 = 2 × 2 × 2 × 2 × 2 = 32
- 2^6 = 2 × 2 × 2 × 2 × 2 × 2 = 64
- 2^7 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128
- 2^8 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
- 2^9 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512
Thus, 2 raised to the power of 9 equals 512.
Key Concept: Exponentiation
Exponentiation is a mathematical operation where a number (called the base) is multiplied by itself a certain number of times, as indicated by the exponent. In the case of 2^9:
- Base: 2 (this is the number that will be multiplied by itself)
- Exponent: 9 (this indicates how many times the base is multiplied by itself)
Exponentiation is a fundamental operation in mathematics and is commonly used in algebra, computer science, physics, and many other fields. Powers of 2, such as 2^9, are especially significant in areas such as digital computing, where binary (base-2) numbers are used to represent data.
In summary, 2^9 = 512, and exponentiation represents repeated multiplication of the base number.