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Chapter 2: Problem 43

Simplify. $$(-10)^{2}$$

Short Answer

Expert verified
100

Step by step solution

01

Identify the Base and Exponent

Observe the expression \((-10)^{2}\). Here, the base is -10 and the exponent is 2.
02

Apply the Exponent to the Base

When an expression is squared, it means the base is multiplied by itself. Therefore, \((-10)^{2} = -10 \times -10\).
03

Multiply the Numbers

Multiply -10 by -10. When you multiply two negative numbers, the result is a positive number. So, \(-10 \times -10 = 100\).

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Key Concepts

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

Simplifying Expressions
Simplifying expressions involves making an equation easier to work with. This often includes performing operations like multiplication, division, addition, and subtraction. When simplifying, you must carefully follow mathematical rules to ensure accuracy. For instance, in the expression \((-10)^2\), the exponent tells us to multiply -10 by itself. By simplifying, we go from a more complex expression to an easier and more understandable form.

The steps to simplify are:
  • Identify the components, such as the base and exponent.
  • Apply the necessary operations, such as multiplication.
  • Combine the results to obtain the simplified expression.
In this case, we end up with 100.
Negative Numbers
Understanding negative numbers is crucial in algebra and arithmetic. Negative numbers are values less than zero and are usually indicated by a minus (-) sign. When dealing with expressions involving negative numbers, it is important to remember the following:
  • Negative times negative equals positive.
  • Negative times positive equals negative.
  • Addition and subtraction rules differ from those of positive numbers.
In \((-10)^2\), the base is a negative number. Multiplying -10 by -10 yields a positive 100 because the product of two negative numbers is positive. Therefore, negative numbers follow specific rules that can simplify calculations.
Multiplication
Multiplication is one of the four fundamental arithmetic operations, alongside addition, subtraction, and division. It is essentially repeated addition. When multiplying, you combine groups of a number to get a total. Key rules for multiplication include:
  • Multiplying two positive numbers gives a positive result.
  • Multiplying two negative numbers gives a positive result.
  • Multiplying a positive number by a negative number gives a negative result.
  • The order in which you multiply numbers doesn't affect the result (commutative property).
In our exercise \((-10)^2\), we apply multiplication to the base -10. The operation \-10 \times -10=100\ shows how multiplication rules for negative numbers work, transforming our original expression to its simplest form.

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