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Chapter 1: Problem 32

Evaluate the powers of \(10 .\) $$10^{2}$$

Short Answer

Expert verified
100

Step by step solution

01

Identify the Base and Exponent

In the expression, the base is 10 and the exponent is 2. This means we need to multiply the base by itself as many times as indicated by the exponent.
02

Apply the Exponent

To evaluate the power, compute the multiplication: \[10^{2} = 10 \times 10\]
03

Perform the Multiplication

Multiply the base by itself: \[10 \times 10 = 100\]

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Key Concepts

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

Base and Exponent
In the expression \(10^2\), we have two parts: the base and the exponent. The base is the number 10. The exponent is the number 2, written as a small number above and to the right of the base. Think of the base as the 'number' and the exponent as the 'how many times' we want to use the 'number' in a multiplication.
For example, in \(10^2\), we are using the base 10 and multiplying it by itself 2 times.
Evaluating Powers
Evaluating the power means calculating the value of the base raised to the exponent. For \(10^2\), we need to find how much 10 multiplied by itself 2 times equals.
Here's how you do it:
  • Start with the base: 10
  • Multiply the base by itself as many times as the exponent tells you: 10 multiplied once by 10
So for \(10^2\), you compute: 10 x 10 = 100.
Therefore, \(10^2 = 100\). This process is what we call evaluating the power of a number.
Multiplication
Multiplication is the mathematical process of combining two numbers to get a product. In the context of powers, multiplication is repeated. For example, \(10^2\) means multiplying 10 by itself: 10 x 10.
Here are some tips for multiplication:
  • Write down both numbers you are multiplying.
  • Start multiplying from the rightmost digit of the bottom number and move to the left.

In the expression \(10^2\), we only multiply two 10s together: 10 x 10 = 100. Therefore, the result of this multiplication is 100. Understanding these steps helps in computing powers accurately.

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