Chapter 4.5, Problem 42E

To determine

To find the value of ‘?’ placed on the exponent part of the numerator ‘a’.

Answer to Problem 42E

8

Explanation of Solution

Given information: $\frac{a^{?}}{a^3}=a^5$

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 $\frac{a^{?}}{a^3}=a^5$

Replace ‘?’ with ‘x’.

Hence, $\frac{a^x}{a^3}=a^5$

  $=>a^x=a^5·a^3$ here, the denominator $(a^3)$ from the left hand side of the equation goes to the right hand side of the equation.

  $=>a^x=a^{5+3}$

  $=>a^x=a^8$

Thus, ‘x’ has a value of 8.