Question

In Exercises 1 and $2,$ make the given changes in the indicated examples of this section, and then simplify the resulting expression. In Example $4(\mathrm{a}),$ change $\left(-x^{2}\right)^{3}$ to $\left(-x^{3}\right)^{2}$

Name: Problem 1, Chapter 1: Basic Technical Mathematics with Calculus
Uploaded: 2021-06-02T10:53:44-08:00
Duration: 2 min 12 s
Channel: Priyanka Sadarangani
Description: In Exercises 1 and 2, make the given changes in the indicated examples of this section, and then simplify the resulting expression. In Example 4(a), change (-x^2)^3 to (-x^3)^2

   In Exercises 1 and $2,$ make the given changes in the indicated examples of this section, and then simplify the resulting expression.
In Example $4(\mathrm{a}),$ change $\left(-x^{2}\right)^{3}$ to $\left(-x^{3}\right)^{2}$

Basic Technical Mathematics with Calculus

Allyn J. Washington,… 11th Edition

Chapter 1, Problem 1

Instant Answer

Solved by Expert Priyanka Sadarangani

06/02/2021

Step 1

This can be written as $(-1 \cdot x^{2})^{3}$ using the property that $(-a)^n = (-1)^n \cdot a^n$. Show more…

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In Exercises 1 and $2,$ make the given changes in the indicated examples of this section, and then simplify the resulting expression. In Example $4(\mathrm{a}),$ change $\left(-x^{2}\right)^{3}$ to $\left(-x^{3}\right)^{2}$

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Key Concepts

Negative Base and Even Exponents

Understanding how negative bases behave is crucial; when a negative number is raised to an even power, the result becomes positive because the negatives pair up and cancel. This concept is key when simplifying expressions where the sign of the factor is affected by the exponent.

Laws of Exponents

These rules govern the manipulation of expressions involving powers, such as the power of a product and the power of a power. They provide guidelines for rewriting expressions in simpler forms by appropriately applying operations like multiplying or distributing exponents.

Power of a Product

This concept states that when a product is raised to an exponent, each factor inside the product is raised to that exponent individually. It is essential when modifying expressions that involve variables and coefficients together, ensuring correct application of the exponent to each factor.

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