Chapter 9, Problem 43SGR

To determine

To calculate: To write the expression using negative exponent

Answer to Problem 43SGR

Expression in negative exponent is $6^{-3}$

Explanation of Solution

Given information: Expression is $\frac{1}{6^3}$

Formula Used:

Exponential identities are

  $x^a{x}^b=x^{a+b}$

  $x^a{y}^a={\left(xy\right)}^a$

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

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

  $x^{-a}=\frac{1}{x^a}$

Calculation:

Expression is given as

  $\frac{1}{6^3}$

Using the exponential identity $x^{-a}=\frac{1}{x^a}$ to write the expression with positive exponent

  $\frac{1}{6^3}=6^{-3}$

Conclusion:

Hence, expression in negative exponent is $6^{-3}$