Chapter 4, Problem 22CT

To determine

To write the expression only using positive exponents ${15}^{-4}$

Answer to Problem 22CT

  ${\left(\frac{1}{15}\right)}^4$

Explanation of Solution

Given information:

Number ${15}^{-4}$

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 ${15}^{-4}$ , the numerator is 15 and the denominator is 1.

The above may also be written as-

  $={\left(\frac{15}{1}\right)}^4$

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

  $={\left(\frac{1}{15}\right)}^4$

So the numerator now becomes 1, the denominator changes to 15, and the exponent becomes positive.

Conclusion-

  $={\left(\frac{1}{15}\right)}^4$