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Chapter 9: Problem 53

Evaluate. $$ 10^{3} $$

Short Answer

Expert verified
1000

Step by step solution

01

Understand the Exponential Form

The expression given is in the form of an exponent, where the base is 10 and the exponent is 3. In general, for a number in the form of \(a^b\), \(a\) is the base and \(b\) is the exponent.
02

Expand the Exponent

An exponent indicates how many times to multiply the base by itself. For \(10^3\), this means multiplying 10 three times: \[ 10^3 = 10 \times 10 \times 10 \].
03

Perform the Multiplication

Now, calculate the value by performing the multiplication: \( 10 \times 10 = 100 \), then \( 100 \times 10 = 1000 \).
04

Write the Final Answer

After completing the multiplication, the value 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.

Exponential Notation
Exponential notation is a way to express repeated multiplication of the same number. It is very useful for simplifying how we write and understand large numbers of multiplications. Instead of writing out a number several times, we use an exponent. For example, instead of writing
10 脳 10 脳 10, we can express this as
103. The small number (3) is called the exponent and it shows how many times you multiply the base (10) by itself. This makes expressions more manageable and less cumbersome to write.
Base and Exponent
In exponential notation, every expression consists of a base and an exponent. The base is the number that you multiply, and the exponent tells you how many times to multiply the base by itself. Let鈥檚 break down the example from the exercise:
  • Base: 10
  • Exponent: 3
In our expression,
103,
10 is the base and 3 is the exponent. This means that you multiply 10 by itself three times. So,
103
means
10 脳 10 脳 10.
Multiplication
When dealing with exponents, understanding multiplication is crucial. Let's break down the example
103
step-by-step:
  • First, calculate 10 脳 10, which equals 100.
  • Next, multiply the result (100) by the base (10) again: 100 脳 10 equals 1000.
Therefore,
103 = 1000.
Multiplying the same number multiple times, as indicated by the exponent, often results in very large numbers, and exponents help simplify this process.

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