/*! 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 43 Evaluate each expression. $$(-... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 43

Evaluate each expression. $$(-5)(-2)^{3}$$

Short Answer

Expert verified
The expression evaluates to 40.

Step by step solution

01

Evaluate the exponent

The expression inside the parentheses is (-2)^3. To evaluate this, take the base (-2) and raise it to the power of 3. (-2) raised to the power of 3 is (-2) * (-2) * (-2).
02

Multiply the base

First, multiply (-2) * (-2), which equals 4. Then, multiply the result by (-2): 4 * (-2) = -8. So, (-2)^3 = -8.
03

Multiply the results

Now take the result from Step 2 (-8) and multiply it by -5: (-5) * (-8) = 40. So, the expression (-5)(-2)^3 evaluates to 40.

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Key Concepts

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

exponents
Exponents are a way of expressing repeated multiplication of a number by itself. For example, in the expression \((-2)^3\), we have an exponent of 3, which means we multiply \(-2\) by itself three times. An exponent is written as a small number to the upper right of the base number.

In this particular expression, \((-2)\) is the base and 3 is the exponent. This tells us to calculate \(-2 \times -2 \times -2\).

When working with exponents:
  • First, identify the base and the exponent.
  • Multiply the base by itself as many times as the exponent indicates.
Understanding exponents is crucial because they often appear in algebraic expressions and equations. They help simplify repeated multiplication into a shorter form.
multiplication in algebra
Multiplication is a key operation in algebra and understanding it is essential for solving expressions. It involves finding the product of numbers. When we multiply, we combine equal groups.

In the example \((-2)^3\), we multiplied \(-2\) by itself three times, resulting in \(-2 \times -2 \times -2 = -8\).

Similarly, to find the final value of the expression \((-5) \times (-8)\), we will multiply these two numbers.

Here鈥檚 a quick guide to multiplication in algebra:
  • Multiply numbers as usual.
  • If multiplying similar terms (like variables), combine them as needed.
Multiplication helps combine values and find their collective amount. It's also important in distributing terms across parentheses and simplifying algebraic expressions.
negative numbers
Negative numbers are numbers less than zero, and they have a few unique properties with arithmetic operations. When dealing with negative numbers, it's important to pay attention to the rules to avoid mistakes.

Here are some tips for working with negative numbers:
  • When multiplying two negative numbers, the result is positive (\(-2 \times -2 = 4\)).
  • When multiplying a negative number by a positive number, the result is negative (\(4 \times -2 = -8\)).
  • Pay close attention to the signs to avoid mixing up positive and negative results.

In our exercise, we first calculated \((-2)^3\) as -8, and then multiplied -8 by -5 to get 40. The negative signs canceled each other out, resulting in a positive product. Understanding how negative numbers interact with each other in operations like multiplication is vital for solving algebra problems correctly.

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