Chapter 9, Problem 38SGR

To determine

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

Answer to Problem 38SGR

Quotient is $k^6$

Explanation of Solution

Given information: Expression is $\frac{k^{10}}{k^4}$

Formula Used:

Exponential identities are

  $x^a{x}^b=x^{a+b}$

  $x^a{y}^a={\left(xy\right)}^a$

  ${\left(x^a\right)}^b={\left(x\right)}^{ab}$

  $\frac{x^a}{x^b}={\left(x\right)}^{a-b}$

Calculation:

Expression is given as

  $\frac{k^{10}}{k^4}$

On solving the above expression using the exponential identity $\frac{x^a}{x^b}={\left(x\right)}^{a-b}$

  $\begin{array}{l}\frac{k^{10}}{k^4}={\left(k\right)}^{10-4}\\ \frac{k^{10}}{k^4}=k^6\end{array}$

Conclusion:

Hence, quotient is $k^6$