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Chapter 1: Problem 33

Evaluate the powers of \(10 .\) $$10^{3}$$

Short Answer

Expert verified
1000

Step by step solution

01

Understanding the exponent

The exponent indicates how many times the base (10) is multiplied by itself. Here, the exponent is 3.
02

Write the multiplication expression

Since the exponent is 3, write the expression as: \(10^3 = 10 \times 10 \times 10\)
03

Perform the multiplication

Multiply the numbers sequentially: 1. First multiplication: \(10 \times 10 = 100\) 2. Then multiply the result by 10: \(100 \times 10 = 1000\)
04

Write the final answer

The result of \(10^3\) is 1000.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exponentiation
Exponentiation is a mathematical operation involving two numbers, the base and the exponent. The base is the number that is being multiplied, while the exponent (also called the power) tells us how many times the base is used as a factor. For example, in the expression \(10^3\), 10 is the base and 3 is the exponent. This means we multiply 10 by itself three times: \(10 \times 10 \times 10\). The process of exponentiation simplifies repeated multiplication, making it easier to work with very large or very small numbers.
Multiplication
Multiplication is one of the basic arithmetic operations and involves calculating the total of one number added repeatedly. For instance, when we have \(10^3\), we need to multiply 10 by 10, and then multiply the result by 10 again. Here鈥檚 the step-by-step process:
  • Start with the first 10 and multiply it by the next 10: \(10 \times 10 = 100\)
  • Take the result (100) and multiply it by the next 10: \(100 \times 10 = 1000\)
Thus, \(10^3\) equals 1000. Breaking down multiplication into smaller steps like this helps in understanding how exponentiation works.
Base and Exponent
Knowing the difference between the base and the exponent is crucial in exponentiation. The base is the main number you begin with. In the expression \(10^3\), 10 is our base. The exponent indicates how many times you multiply the base by itself. Here, the exponent is 3. This can be written mathematically as \(10^3 = 10 \times 10 \times 10\). Understanding this notation helps you solve problems involving powers of ten, as well as more complex exponentiation equations. Remember:
  • The base is the number being multiplied.
  • The exponent tells you how many times to multiply the base by itself.
This concise understanding streamlines calculations involving powers of ten and other bases.

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