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When you square a negative number, you are essentially multiplying the number by itself. In mathematical terms, squaring any number, whether positive or negative means raising it to the power of 2. For example, in the expression \[(-1.3)^2\], the base is -1.3, and the exponent is 2. As part of the process:

• First, you need to identify the base and the exponent.
• Next, you multiply the base by itself.

Specifically:
\[(-1.3) \times (-1.3)\] When you multiply two negative numbers, the result is always a positive number. Thus, \[(-1.3) \times (-1.3) = 1.69\]. This is important because many students often misunderstand or misapply the rules for negative numbers in exponents.
To summarize, remember that squaring a negative number cancels out the negative sign, resulting in a positive number.

Multiplication is a fundamental arithmetic operation, and understanding its rules is crucial for solving algebraic expressions successfully. One common rule in multiplication involving negative numbers is:

• Multiplying two negative numbers always gives a positive result.
• Multiplying a positive number by a negative number results in a negative number.
• Multiplying two positive numbers yields a positive number.

Applying these rules can help simplify complex expressions. In the example of \[(-1.3) \times (-1.3)\], the two negative signs cancel each other out, giving a positive outcome. Therefore, \[(-1.3) \times (-1.3) = 1.69\].
Knowing these rules makes it easier to predict and verify results in any multiplication involving positive and negative numbers.

Basic algebra serves as a foundation for more advanced mathematical concepts. It typically involves operations of addition, subtraction, multiplication, and division with algebraic expressions. Here are a few key elements:

• Variables: Symbols that represent unknown values and can vary.
• Coefficients: Numbers that multiply the variables.
• Constants: Fixed numbers without variables.
• Exponents: Indicate how many times a number (the base) is multiplied by itself.

In the given example \[(-1.3)^2\], the exponent (2) instructs us to multiply -1.3 by itself. Understanding the interaction between bases, exponents, and multiplication is crucial. Practice with these basic concepts helps enhance problem-solving skills and builds a strong arithmetic foundation.