/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 Expand the exponential expressio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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: \(6^2 = 6 \times 6\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

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.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For each English sentence, write a mathematical expression and simplify. Find the quotient of 1890 and 45.

Simplify expression. Then identify the dividend, divisor, and quotient. \(8 \longdiv { 6 4 }\)

Multiply. $$\begin{array}{r} 1410 \\ \times 8 \\ \hline \end{array}$$

Convert the numbers to expanded form. $$7089$$

Shawn's scores on his last four tests were \(83,95,87,\) and \(91 .\) What is his average for these tests?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.