Chapter ISG, Problem 7.1.1P

a.

To determine

To explain correct statement

Answer to Problem 7.1.1P

1^st statement is correct.

Explanation of Solution

Given:

  $g^{5}g{h}^6=(g.g.g.g.g).(g).(h.h.h.h.h.h)$

  $g^{5}g{h}^6=(g.g.g.g.g).(gh.gh.gh.gh.gh.gh)$

Here, the 1^st statement is correct because it is expanded in a correct manner. The 2^nd statement is incorrect because that expansion would be correct if $g^5{(gh)}^6$ would have been the term.

b.

To determine

To simplify $g^{5}g{h}^6$

Answer to Problem 7.1.1P

  ${(gh)}^6$ is the simplified form.

Explanation of Solution

Given:

Term: $g^{5}g{h}^6$

Calculation:

Theterm is expanded as $(g.g.g.g.g).(g).(h.h.h.h.h.h)$

But, it can be written as $(g.g.g.g.g.g).(h.h.h.h.h.h)$

Simplifying it,

  $g^{5}g{h}^6$ = $g^6{h}^6$

Again,

  $g^6{h}^6$ = ${(gh)}^6$