Chapter 4.5, Problem 44E

To determine

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

Answer to Problem 44E

1

Explanation of Solution

Given information: an equation to find the value placed on the question mark.

Given, $b^{?}·b^6=b^7$

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 $b^{?}·b^6=b^7$

Replace ‘?’ with ‘x’.

Hence, $b^x·b^6=b^7$

  $=>b^x=\frac{b^7}{b^6}$

Here, $b^6$ from the left hand side of the equation goes to the right hand side of the equation.

  $=>b^x=b^{7-6}$ Using the product of power rule.

  $=>b^x=b^1$

Thus, ‘x’ has a value of 1.