Chapter 9, Problem 11PT

To determine

To calculate:To find product or quotient and express using exponents for the below expression:

  ${\left(-2\right)}^5÷{\left(-2\right)}^2$

Answer to Problem 11PT

The quotient of the expression ${\left(-2\right)}^5÷{\left(-2\right)}^2$ is ${\left(-2\right)}^3$ .

Explanation of Solution

Given information:

Given expression is ${\left(-2\right)}^5÷{\left(-2\right)}^2$

Formula Used:

Quotient rule of the exponent states that “when dividing two powers that have the same base, exponents can be subtracted”:

  $a^m÷a^n=a^{m-n}$

Calculation:

Given expression is ${\left(-2\right)}^5÷{\left(-2\right)}^2$

Using the above explanation for the Quotient rule of the exponent, we have:

  ${\left(-2\right)}^5÷{\left(-2\right)}^2={\left(-2\right)}^{5-2}$

Solving the above equation, we have:

  ${\left(-2\right)}^5÷{\left(-2\right)}^2={\left(-2\right)}^3$

Thus, the Quotient of the expression ${\left(-2\right)}^5÷{\left(-2\right)}^2$ is ${\left(-2\right)}^3$ .

Conclusion:

The Quotient of the expression ${\left(-2\right)}^5÷{\left(-2\right)}^2$ is ${\left(-2\right)}^3$ .