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Chapter 2: Problem 44

Simplify. $$(-8)^{2}$$

Short Answer

Expert verified
64

Step by step solution

01

Understand the Problem

The problem requires simplifying \((-8)^2\). This means we need to find the value of -8 raised to the power of 2.
02

Apply the Exponent Rule

Recall the exponent rule which states that \[a^b = a \times a \times ... \times a \] (b times). For \((-8)^2\), this means we multiply -8 by itself.
03

Perform the Multiplication

Calculate \((-8) \times (-8)\). Multiplying two negative numbers results in a positive number, so \(-8 \times -8 = 64\).

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Key Concepts

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

Exponent rules
Understanding exponent rules is essential when working with powers. An exponent tells us how many times to multiply a number by itself. For instance, in the expression \((-8)^2\), the exponent is 2. This indicates we should multiply -8 by itself two times.

The general rule is \[a^b = a \times a \times ... \times a\text{ (b times)}\].

Here, \(a\) is the base, and \(b\) is the exponent. When the exponent is 2, this is often called 'squaring' the base. Such clear rules make exponents predictable and convenient to use.
Negative numbers
Dealing with negative numbers can seem tricky, but it follows specific rules. When multiplying negative numbers:
  • If you multiply a negative by another negative, you get a positive. For example, (-8) 脳 (-8) = 64.
  • If you multiply a negative by a positive, the result is negative. For instance, (-8) 脳 2 = -16.
Remember: when squaring a negative number \[ (a^2) \] (as in \((-8)^2\)), the result will always be positive since it involves two negative multiplications canceling out.
This maintains clarity and consistency in calculations.
Multiplication
Multiplication is the process of repeated addition of the same number. When working with exponents, you extend this concept. For example, in \((-8)^2\), you multiply -8 by itself:
\((-8) \times (-8)\)
Using the rules of negative numbers, a negative times a negative equals a positive, giving you 64.

Practicing such multiplications helps reinforce the understanding of how exponents operate, especially when involving negative bases. Mastery of this will help simplify more complex algebraic expressions.

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Most popular questions from this chapter

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