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Chapter 2: Problem 16

Identify the base and the exponent in each. $$(13 k)^{3}$$

Short Answer

Expert verified
In the expression \((13k)^3\), the base is \(13k\) and the exponent is \(3\).

Step by step solution

01

Identify the Base

In the expression \((13k)^3\), the base is the term inside the parentheses: \(13k\).
02

Identify the Exponent

In the expression \((13k)^3\), the exponent is the term outside the parentheses: \(3\). So in the expression \((13k)^3\), the base is \(13k\) and the exponent is \(3\).

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Key Concepts

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

Base and Exponent
Understanding the concept of base and exponent is crucial when dealing with expressions involving powers. In an expression like \[(13k)^3\],the base is the number or expression that is multiplied by itself. The exponent indicates how many times the base is used as a factor. In this example:
  • The base is \(13k\). This means that \(13k\) is going to be multiplied by itself a total of three times.
  • The exponent is \(3\). This tells us the number of times the multiplication is performed.
When you see an expression in the form of \(a^b\), you can always identify \(a\) as the base and \(b\) as the exponent. This helps in simplifying and solving mathematical expressions efficiently.
Algebraic Expressions
An algebraic expression is a combination of numbers, variables, and operations. In mathematics, understanding how to work with algebraic expressions is essential. They are used to represent real-world problems in a mathematical form.In our expression\[(13k)^3\], \(13k\) itself is an algebraic expression. Here we have:
  • A constant: \(13\), which is a fixed number.
  • A variable: \(k\), which can represent different numbers. This variable allows for flexibility and can be adjusted to represent different scenarios.
When working with algebraic expressions, operations like addition, subtraction, multiplication, and division are applied to simplify or solve them. Expressions like \((13k)^3\) show us how algebra combines constants and variables to create a flexible and powerful mathematical language.
Mathematics Education
Teaching concepts like base and exponent or algebraic expressions can sometimes be challenging. It's important to break these down into smaller, understandable parts. Effective mathematics education often involves:
  • Hands-on Activities: Use visual aids or manipulatives to make abstract concepts more concrete for students. For example, use cubes to physically represent powers in order to grasp the concept of multiplication involved with exponents.
  • Step-by-Step Approach: Always follow a structured method to solve problems, such as identifying each component in expressions like bases and exponents. This creates a clear path to understanding.
  • Real-world Applications: Connect algebraic expressions to real-world scenarios to make learning relevant and engaging. Explain how variables might represent different quantities in practical situations.
These strategies help unlock the complexities of mathematical ideas, making them accessible and enjoyable for students. By fostering a strong understanding of these foundational concepts, students can build a more comprehensive knowledge base for future learning in mathematics.

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Most popular questions from this chapter

Simplify the expression using the product rule. Leave your answer in exponential form. $$(-3) \cdot(-3)^{5} \cdot(-3)^{2}$$

Perform the operation as indicated. Write the final answer without an exponent. \(\left(3.19 \times 10^{-5}\right)+\left(9.2 \times 10^{-5}\right)\)

Simplify the expression using one of the power rules. $$\left(\frac{d}{c}\right)^{8}$$

Express each number in scientific notation, then solve the problem. Humans shed about \(1.44 \times 10^{7}\) particles of skin every day. How many particles would be shed in a year? (Assume 365 days in a year.)

Simplify the expression using the product rule. Leave your answer in exponential form. $$\left(\frac{7}{10} y^{9}\right)\left(-2 y^{4}\right)\left(3 y^{2}\right)$$
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