What’s -1 Squared? Understanding the Basics of Exponents
Introduction
Exponents are a fundamental concept in mathematics that are used to represent repeated multiplication of a number. They are commonly used in algebra, calculus, and other advanced math subjects. In this article, we will focus on the basics of exponents and answer the question, “What’s -1 squared?”
What are Exponents?
An exponent is a small number written above and to the right of a base number. The exponent tells you how many times to multiply the base number by itself. For example, 2^{3} means 2 multiplied by itself three times, or 2 x 2 x 2 = 8.
Exponents are a shorthand way of writing repeated multiplication. They are useful for simplifying complex calculations and expressing large or small numbers in a compact form.
How to Solve Exponent Problems
To solve an exponent problem, you need to know the base number and the exponent. Then, you simply multiply the base number by itself the number of times indicated by the exponent.
For example, to solve 2^{4}, you would multiply 2 x 2 x 2 x 2, which equals 16. To solve 3^{2}, you would multiply 3 x 3, which equals 9.
It’s important to remember that exponents follow the order of operations, which means they are evaluated before multiplication, division, addition, and subtraction. If there are multiple exponents in an equation, you should solve them from left to right.
What’s -1 Squared?
Now that we understand the basics of exponents, let’s answer the question, “What’s -1 squared?”
To solve this problem, we need to multiply -1 by itself twice, since the exponent is 2. When we multiply a negative number by itself, the result is always positive. So, -1 x -1 = 1. Therefore, -1^{2} = 1.
It’s important to note that the order of operations applies to negative exponents as well. For example, (-2)^{-3} means the reciprocal of -2 cubed, or -1/8.
Conclusion
Exponents are a powerful tool in mathematics that allow us to represent repeated multiplication in a compact form. By understanding the basics of exponents, we can solve a wide range of problems and simplify complex calculations. Now that you know what -1 squared means, you’re ready to tackle more advanced exponent problems!
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