Question

Simplify each number. $$-(-27)^{-\frac{4}{3}}$$

   Simplify each number.
$$-(-27)^{-\frac{4}{3}}$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 7, Problem 60

Instant Answer

Solved by Expert Emma Chickles

08/12/2019

Step 1

So, we have: $$-(-27)^{-\frac{4}{3}} = -(-3^3)^{-\frac{4}{3}}$$ Show more…

Show all steps

lock

Thanks for your feedback!

Simplify each number. $$-(-27)^{-\frac{4}{3}}$$

Play audio

Feedback

Powered by NumerAI

Emma Chickles and 92 other subject Calculus 3 educators are ready to help you.

Ask a new question

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

Negative Exponents

The rule of negative exponents transforms an expression a?? into its reciprocal form, 1/(a?), for any nonzero a. It is a key tool for rewriting and simplifying expressions that involve inverse relationships, making further operations more straightforward.

Rational Exponents

Rational exponents express powers in fractional form, where the denominator indicates the type of root (such as a cube root for 1/3) and the numerator indicates the power to which the result is raised. This form helps in converting between radical notation and exponent notation, allowing for more versatile manipulation of expressions.

Properties of Exponents

The laws governing exponents, including the product, quotient, and power rules, enable efficient simplification and manipulation of expressions with exponential terms. These properties allow for grouping and redistributing exponents, ensuring that expressions can be simplified step by step in a consistent manner.

Handling Negative Bases with Rational Exponents

When a negative base is raised to a fractional exponent, it is crucial to check the parity of the denominator in the fraction. If it is an odd number, the corresponding root is defined in the set of real numbers since odd roots of negative numbers exist; if it is even, the result may not be a real number. This consideration ensures that the simplification remains valid within the real number system.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later