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Chapter 1: Problem 13

\((-1.2)^{3}\)

Short Answer

Expert verified
The result of \((-1.2)^{3}\) is -1.728.

Step by step solution

01

Understanding the Problem

This is a simple exponentiation problem. The base is -1.2 and the exponent is 3. This means you need to multiply the base, -1.2, by itself twice.
02

Performing the First Multiplication

First, multiply -1.2 by itself. The multiplication of two negative numbers yields a positive result. Thus, \(-1.2 \times -1.2 = 1.44\).
03

Performing the Second Multiplication

Now, multiply the result, 1.44, by -1.2. The multiplication of a positive number and a negative number yields a negative result. Thus, \(1.44 \times -1.2 = -1.728\).

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero, often represented with a minus sign (-) in front of them. When dealing with negative numbers, it's important to understand how they interact during operations such as addition, subtraction, multiplication, and division.
  • A negative number multiplied by another negative number results in a positive number. For example, (-1) 脳 (-1) = 1.
  • A negative number multiplied by a positive number or vice versa results in a negative number. For instance, (-1) 脳 2 = -2.
This duality of signs is crucial when solving problems that involve negative numbers. Remembering these rules helps in simplifying expressions and ensuring accurate outcomes.
Multiplication
Multiplication is a fundamental arithmetic operation where we calculate the total of one number added repeatedly. Understanding the multiplication rules with negative numbers can make your math journey smoother.
When multiplying numbers, here is how it works:
  • Multiplying two positive numbers results in a positive number.
  • Multiplying two negative numbers results in a positive number due to the canceling effect of two negatives.
  • Multiplying a positive number by a negative gives a negative result, aligning with the basic properties of numbers.
It's essential to keep track of these rules to solve multiplication problems accurately, especially in algebra.
Algebra
Algebra is the branch of mathematics dealing with symbols and the rules for manipulating those symbols. These symbols can represent numbers and quantities in formulas and equations, often manipulated through basic operations such as addition, subtraction, multiplication, and division.
Exponentiation, the operation seen in the exercise where a number (the base) is multiplied by itself several times (indicated by the exponent), is a key concept in algebra.
  • Understanding exponentiation is essential as it helps simplify large numbers and expressions.
  • When the base is negative, such as (-1.2) in the exercise, knowing how the number behaves under multiplication is critical.
Algebraic skills are vital for solving equations, performing operations, and understanding higher-level math concepts.

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