Chapter 2.1, Problem 1E

Solution

(a.)

The name of the property $a^m\cdot a^n=a^{m+n}$ .

Name of the property is product of power.

Given:

  $a^m\cdot a^n=a^{m+n}$

Concept Used:

Product of power.

Calculation:

Therefore, the property used in $a^m\cdot a^n=a^{m+n}$ is product of power.

(b.)

The name of the property $a^{-m}=\frac{1}{a^m}$

  $a\ne 0$ .

Name of the property is Negative Exponent.

Given:

  $a^{-m}=\frac{1}{a^m}$

  $a\ne 0$

Concept Used:

Negative Exponent.

Calculation:

Therefore, the property used in $a^{-m}=\frac{1}{a^m}$

  $a\ne 0$ is negative exponent.

(c.)

The name of the property of ${\left(ab\right)}^m=a^m\cdot b^m$ .

Name of properties is power of a product.

Given:

  ${\left(ab\right)}^m=a^m\cdot b^m$

Concept Used:

power of a product.

Calculation:

Therefore, the property used in ${\left(ab\right)}^m=a^m\cdot b^m$ is power of product.