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Chapter 1: Problem 42

Write each expression without using exponents. $$y^{4}$$

Short Answer

Expert verified
The expression \(y^{4}\) can be rewritten without exponents as \(y \cdot y \cdot y \cdot y\).

Step by step solution

01

Understanding Exponents

An expression like \(y^{4}\) signifies that the base, \(y\), is multiplied by itself for the number of times indicated by the exponent, which in this case is 4.
02

Rewriting the Expression

Therefore, \(y^{4}\) can be rewritten as \(y \cdot y \cdot y \cdot y\), meaning that \(y\) is multiplied by itself 4 times.

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Key Concepts

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

Understanding Algebra
Algebra is a fundamental branch of mathematics. It involves using symbols and letters to represent numbers and quantities in equations and formulas. This abstraction allows us to solve problems more flexibly. Often, in algebra, we deal with unknown values and represent them with variables like \(x\) or \(y\).
Variables stand in for numbers and help us construct general formulas and solve a wide range of problems. Algebraic operations follow basic arithmetic rules but include powerful techniques to simplify and solve equations, such as combining like terms and applying the distributive property.
Demystifying Expressions
Expressions are combinations of numbers, variables, and operations (like addition or multiplication). They don't have an equality sign, unlike equations. For example, \(y^4\) is an expression that involves the variable \(y\) and an exponent, indicating that \(y\) is multiplied by itself four times.
  • Variables: Represent unknown values.
  • Coefficients: Numbers multiplying the variables, such as "4" in "4y".
  • Terms: Parts of an expression separated by '+' or '-' signs.
Expressions can be simplified or evaluated depending on the given values for variables. Simplifying expressions using algebraic rules can make them easier to work with.
Cracking the Code: Mathematical Notation
Mathematical notation is the system of symbols used to express mathematical ideas concisely and clearly. It's like learning a new language that helps us communicate complex concepts efficiently. In expressions, notation like \(y^4\) uses:
  • Exponents: Tells how many times a number, the base, is multiplied by itself.
  • Operators: Symbols like \(+\), \(-\), \(\cdot\), which indicate mathematical operations.
Mathematical notation makes it easier to grasp and manipulate mathematical concepts. Understanding how to read and write in this symbolic language is key to succeeding in mathematics.

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Most popular questions from this chapter

Which property of real numbers justifies each statement? $$9 \cdot \frac{1}{9}=1$$

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If the values of both \(x\) and \(y\) were doubled, what would happen to the value of \(5 x y^{2} ?\)
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