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Chapter 1: Problem 18

Expand the exponential expression as a repeated multiplication. Do not simplify. $$6^{2}$$

Short Answer

Expert verified
6^2 = 6 \times 6

Step by step solution

01

Understand the Exponent

Identify the base and the exponent in the expression. Here, the base is 6 and the exponent is 2.
02

Interpret the Exponentiation

Understand that an exponent indicates how many times to multiply the base by itself. Since the exponent is 2, it means multiplying the base (6) by itself twice.
03

Write the Repeated Multiplication

Write the expression as a repeated multiplication: \(6^2 = 6 \times 6\)

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Key Concepts

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

Exponents
Exponents are a way to represent repeated multiplication of the same number. When you see an expression like \(6^2\), the small number (2) is the exponent. It tells you how many times to multiply the base (6) by itself. Exponents make it easier to write large numbers and perform calculations. Instead of writing 6 \times 6, we write 6\^2. This is not only shorter but also helps us understand the structure of the number better.

An exponent implies a certain number of multiplications. For instance:
  • \(3^3\) means 3 \times 3 \times 3
  • \(2^4\) means 2 \times 2 \times 2 \times 2

      • So, once you understand what the exponent represents, working with these expressions becomes very straightforward.
Base and Exponent
In an expression like \(6^2\), we have two important parts: the base and the exponent. Here:
  • Base: The base is the number that is being multiplied. In \(6^2\), the base is 6.
  • Exponent: The exponent tells you how many times to multiply the base by itself. In \(6^2\), the exponent is 2.

      • Understanding the role of each part helps in simplifying and expanding exponential expressions. Let鈥檚 break down the example \(6^2\) further:
      • Identify the base: Look for the larger number or the main number in the expression, which is 6 here.
      • Identify the exponent: Look for the small number written at the upper-right corner of the base, which is 2 in this case.
      • Combine them: The exponent shows that 6 should be multiplied by itself 2 times (6 \times 6).
Repeated Multiplication
To expand an exponent, you multiply the base by itself a given number of times. Let鈥檚 take the exercise you have and see how it works in detail.

When the expression is \(6^2\), you can break it down as:
  • Step 1: Identify that 6 is the base and 2 is the exponent.
  • Step 2: Understand that the exponent 2 means you will multiply the base (6) by itself twice.
  • Step 3: Write it as repeated multiplication: \ \(6^2 = 6 \times 6\)

      • So in very simple terms, \(6^2\) can directly be written as 6 multiplied by 6, which is \(6 \times 6\). This method applies to any exponential expression, regardless of the base and exponent. It鈥檚 essential to get comfortable with repeated multiplication as it is the foundation for understanding more complex math concepts.

      Remember: The exponent tells you exactly how many times the base will be multiplied by itself. By following these steps, you can easily expand any exponential expression.

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Most popular questions from this chapter

Convert the number to standard form. Two hundred forty-eight thousand

Fill in the blank with the inequality symbol \(<\) or \(>\). $$0 \square 3$$

Fill in the blank with the inequality symbol \(<\) or \(>\). $$28 \square 30$$

Perform the indicated operation by using a calculator. $$\begin{array}{r} 9,300,050 \\ 7,803,513 \\ 3,480,009 \\ +\quad 907,822 \\ \hline \end{array}$$

Write the number in words. $$108$$
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