Evaluate the expression. [(-(1)/(3))^2]^-3

Name: Problem 12, Chapter 1: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-05-05T22:52:25-08:00
Duration: 1 min 11 s
Channel: Tyler Moulton
Description: Evaluate the expression. [(-(1)/(3))^2]^-3

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Even Exponents and Squaring Negative Numbers

When a negative number is raised to an even exponent, the result is a positive number because the negative signs cancel out in pairs. This principle is important when dealing with expressions involving negative bases, especially when such bases are raised to even powers, assuring that the negative sign does not affect the outcome.

Power of a Power Rule

The power of a power rule states that when an exponential expression is raised to another power, the exponents are multiplied. In other words, (a^m)^n equals a^(m*n). This rule is particularly useful for simplifying complex exponential expressions and is a fundamental property in the study of exponents.

Exponentiation

Exponentiation is the operation of raising a number, known as the base, to a power, which is the exponent. It involves repeated multiplication of the base by itself. This concept forms the foundation for understanding expressions that involve powers and is used in various areas of mathematics.

Negative Exponents

A negative exponent indicates that the base should be taken as the reciprocal and then raised to the corresponding positive exponent. This means that a term like a^(-n) is equivalent to 1/(a^n), provided that a is non-zero, making it a useful tool for simplifying expressions that contain negative exponents.

Transcript

Please give Ace some feedback