What is 3 to the 5th power?
The correct answer and explanation is:
Correct Answer:
3 to the 5th power is 243.
Explanation (Approximately 300 Words):
Exponentiation is a mathematical operation that involves raising a base number to a certain power. The notation “3 to the 5th power” is written as: 353^5
This means you multiply the number 3 by itself a total of 5 times: 35=3×3×3×3×33^5 = 3 \times 3 \times 3 \times 3 \times 3
Let’s break it down step by step:
- Step 1: 3×3=93 \times 3 = 9
- Step 2: 9×3=279 \times 3 = 27
- Step 3: 27×3=8127 \times 3 = 81
- Step 4: 81×3=24381 \times 3 = 243
So, 35=2433^5 = 243.
Understanding Exponents:
The number 3 is called the base, and 5 is called the exponent or power. The exponent tells us how many times to multiply the base by itself.
This is different from multiplication or addition. For example, while multiplication is repeated addition, exponentiation is repeated multiplication. 31=332=3×3=933=3×3×3=2734=3×3×3×3=8135=2433^1 = 3 \\ 3^2 = 3 \times 3 = 9 \\ 3^3 = 3 \times 3 \times 3 = 27 \\ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \\ 3^5 = 243
As the exponent increases, the result grows much faster. This is called exponential growth.
Applications:
Exponents are used in many fields, such as:
- Science (e.g., calculating energy, sound intensity)
- Finance (e.g., compound interest)
- Computer science (e.g., algorithm complexity, binary systems)
So, 3 to the 5th power is 243, and it’s a great example of how quickly numbers can grow when repeatedly multiplied by themselves.