Chapter 4.5, Problem 2E

To determine

To provide example of quotient of powers property.

Answer to Problem 2E

  $\frac{a^x}{a^y}=a^{x-y},a\ne 0$

Explanation of Solution

Calculation:

When you divide powers with the same base you just have to subtract the exponents. When you raise a quotient to a power you raise both the numerator and the denominator to the power.This is called the power of a quotient power.

  $\frac{a^x}{a^y}=a^{x-y},a\ne 0$

Now, as an example $\frac{8^7}{8^5}$ is given.

So,

  $\frac{8^7}{8^5}=8^{7-5}$

Hence,

  $\frac{8^7}{8^5}=8^2$