Chapter 7.3, Problem 7LC

To determine

To explain: The comparison between the property for raising a power to a power and the property for multiplying powers with the same base.

Explanation of Solution

Given information: The given property of exponents are raising a power to a power and multiplying powers having the same base.

The property of exponents raising a power to a power represents the multiplication of exponents with the same base.

  ${\left(x^m\right)}^n=x^{\left(m\times n\right)}$

The multiplying powers having the same base represents addition of the exponents with a common base.

  $x^m\times x^n=x^{m+n}$

The comparison of both rule shows that the base remains same in both the properties after the solution.

The contrast between both properties is that the exponents are multiplied when power raise to a power and exponents are added when multiplying powers having the same base.