Chapter 4, Problem 38CR

To determine

To write the expression only using positive exponents ${12}^{-4}$

Answer to Problem 38CR

  ${\left(\frac{1}{12}\right)}^4$

Explanation of Solution

Given information:

Number ${12}^{-4}$

Formula Used: Negative Exponent Rule

Calculation:

The Negative Exponent Rule says that when the exponents are negative, the numerator gets moved to the denominator and makes the exponent positive.

In the number ${12}^{-4}$ , the numerator is 12 and the denominator is 1.

The above may also be written as-

  $\begin{array}{l}\\ {\left(\frac{12}{1}\right)}^{-4}\end{array}$

On applying the negative exponent rule, the numerator & denominators will be reversed, and the exponent will become positive.

  ${\left(\frac{1}{12}\right)}^4$

So the numerator now becomes 1, the denominator changes to 12, and the exponent becomes positive.

Conclusion-

  ${\left(\frac{1}{12}\right)}^4$