Chapter 4, Problem 25CT

To determine

To write the expression only using positive exponents $m^{-4}{n}^5$

Answer to Problem 25CT

  ${\left(\frac{1}{m}\right)}^4{n}^5$

Explanation of Solution

Given information:

Number $m^{-4}{n}^5$

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 $m^{-4}{n}^5$ , the numerator is m and the denominator is 1.

The above may also be written as-

  $m^{-4}{n}^5={\left(\frac{m}{1}\right)}^{-4}{n}^5$

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

  $={\left(\frac{1}{m}\right)}^4{n}^5$

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

Conclusion-

  $={\left(\frac{1}{m}\right)}^4{n}^5$