step 1 All right, guys, for 34 wants me to go ahead and simplify the expression of negative two thirds,

Question

$$\left(-\frac{2}{3 b}\right)^{4}$$

Name: Problem 34, Chapter 5: Algebra for College Students
Uploaded: 2020-04-19T20:21:13-08:00
Duration: 46 s
Channel: Coach Rye
Description: (-(2)/(3 b))^4

   $$\left(-\frac{2}{3 b}\right)^{4}$$

Algebra for College Students

Mark Dugopolski 5th Edition

Chapter 5, Problem 34

Instant Answer

Solved by Expert Coach Rye

04/19/2020

Step 1

Each of these parts will be raised to the power of $4$. $$\left(-\frac{2}{3 b}\right)^{4} = (-2)^4 \cdot (3)^{-4} \cdot (b)^{-4}$$ Show more…

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$$\left(-\frac{2}{3 b}\right)^{4}$$

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Key Concepts

Exponentiation Rules

This concept involves applying a power to an entire expression, meaning that every factor in the expression, whether in the numerator or denominator, is raised to the given power. It is fundamental for simplifying expressions and understanding the distribution of exponents over multiplication and division.

Negative Base with Even Exponent

A key property of negative numbers is that when a negative number is raised to an even exponent, the result is positive. This happens because multiplying an even number of negative factors cancels out the negative signs, resulting in a positive product.

Power of a Fraction

This principle states that when a fraction is raised to a power, both the numerator and the denominator are raised to that power. It enables a systematic approach to simplifying and working with fractional expressions raised to an exponent.

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