In the following exercises, simplify. (a) (-100)^(1)/(2) (b) -100^(1)/(2) (100)^-(1)/(2)

Name: Problem 548, Chapter 9: Elementary Algebra
Uploaded: 2021-07-19T20:11:46-08:00
Duration: 1 min 56 s
Channel: Julie Silva
Description: In the following exercises, simplify. (a) (-100)^(1)/(2) (b) -100^(1)/(2) (100)^-(1)/(2)

step 1 In this problem, we're being asked to simplify each expression. We'll notice each problem is wri

In the following exercises, simplify. (a) (-100)^(1)/(2) (b)...

Key Concepts

Negative Exponents

Negative exponents denote the reciprocal of the base raised to the corresponding positive exponent. In the expression (100)^(-1/2), the negative exponent indicates taking the reciprocal of the square root of 100, leading to 1 divided by the square root of 100. This rule is widely used in algebra to simplify and manipulate expressions involving exponents.

Complex Numbers

Complex numbers extend the real number system to include solutions to equations that do not have real roots, such as the square roots of negative numbers. The square root of a negative number is expressed in terms of the imaginary unit i, where i^2 = -1. This concept is central in understanding how to handle and simplify expressions like (-100)^(1/2).

Order of Operations

The placement of parentheses can change the meaning of an expression significantly. For instance, (-100)^(1/2) means taking the square root of -100, whereas -100^(1/2) means negating the square root of 100. Recognizing how to correctly interpret and apply operations based on parentheses is crucial for simplifying expressions and avoiding common errors.

Fractional Exponents

Fractional exponents represent roots of numbers. For example, an exponent of 1/2 corresponds to the square root of a number, and in general, the expression a^(m/n) represents the nth root of a raised to the mth power. This concept is fundamental in algebra and calculus when dealing with equations and functions involving radical expressions.

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