Chapter 4, Problem 20CT

To determine

To write the fraction in simplest form $\frac{7^6}{7^9}$

Answer to Problem 20CT

  $\frac{1}{7^3}$

Explanation of Solution

Given information:

Expression $\frac{7^6}{7^9}$

Formula Used: Quotient rule with same base and Negative Exponent Rule

Calculation:

The Quotient Rule with same base says that when the bases are same and in division, the exponent powers are subtracted. In the given expression, have the base as 7.

On applying the Quotient Rule, get-

  $\frac{7^6}{7^9}=7^{6-9}$

This will give us-

  $=7^{-3}$

Since exponents should never be negative, apply the negative exponent rule and reverse the numerator & denominator. Hence,

  $=\frac{1}{7^3}$

Conclusion-

  $=\frac{1}{7^3}$