Chapter 4.5, Problem 43E

To determine

To findthe value of ‘?’ placed on the exponent part of the base ‘y’.

Answer to Problem 43E

2

Explanation of Solution

Given information:

Given, $y^5·y^{?}=y^7$

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 $y^5·y^{?}=y^7$

Replace ‘?’ with ‘a’.

Hence, $y^5·y^a=y^7$

  $=>y^a=\frac{y^7}{y^5}$ Here, the numerator $(y^5)$ from the left hand side of the equation goes to the right hand side of the equation.

  $=>y^a=y^{7-5}$ Using the product of power rule.

  $=>y^a=y^2$

Thus, ‘a’ has a value of 2.