Question

If $2^{x}=3,$ what does $4^{-x}$ equal?

   If $2^{x}=3,$ what does $4^{-x}$ equal?

Algebra and Trigonometry

Algebra and Trigonometry

Michael Sullivan 10th Edition

Chapter 6, Problem 84

Instant Answer

Solved by Expert James Kiss

06/14/2020

Step 1

We need to find the value of $4^{-x}$. Show more…

Show all steps

lock

Thanks for your feedback!

If $2^{x}=3,$ what does $4^{-x}$ equal?

Play audio

Feedback

Powered by NumerAI

James Kiss and 86 other subject Algebra 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

Exponentiation

Exponentiation is the process of raising a number (the base) to a power (the exponent). It is fundamental in algebra and allows for expressing large numbers compactly as well as understanding the growth behavior in functions. In many problems, manipulating expressions with exponents requires a firm grasp of how exponents work in order to simplify and solve equations.

Properties of Exponents

The properties of exponents include rules such as the product of powers, power of a power, and negative exponents. These rules enable the simplification of expressions by combining or splitting exponent terms. For example, rewriting expressions by changing the base or handling negative exponents as indicators of reciprocation is essential in solving exponential equations.

Rewriting Bases

Rewriting bases involves expressing an exponential term with a preferred base that matches other terms in an equation. This technique is critical when relationships between exponents need to be identified or when expressions must be simplified. It allows one to uniformly apply the properties of exponents across a problem by ensuring that the terms have a common base.

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