Chapter 4.5, Problem 45E

To determine

To find the value of ‘?’ placed on the exponent part of the base ‘z’.

Answer to Problem 45E

3

Explanation of Solution

Given information:An equation wherein it is required to find the value placed on the question mark.

Given, $\frac{z^7}{z^{?}}=z^4$

This answer shall be derived using the product of powers rule, wherein the exponents of a common base can be added during multiplication and subtracted during division.

Here, it is given that $\frac{z^7}{z^{?}}=z^4$

Replace ‘?’ with ‘a’.

Hence,

  $=>\frac{z^7}{z^a}=z^4$

  $=>z^7=z^a·z^4$

Here, the denominator $(z^a)$ from the left hand side of the equation goes to the right hand side of the equation.

  $=>z^7=z^{a+4}$

  $=>7=a+4$ Using the product of power rule.

  $=>7-4=a$

  $=>a=3$

Thus, ‘a’ has a value of 3.