Determine whether the statement is true or false.
-$$\text { If } \mathrm { a } \mathrm { b } \mathrm { c } \text {, then the greatest common factor of } \mathrm { p } ^ { \mathrm { a } } \mathrm { q } ^ { \mathrm { b } } , \mathrm { p } ^ { \mathrm { b } } \mathrm { q } ^ { \mathrm { c } } \text {, and } \mathrm { p } ^ { \mathrm { c } ^ { \mathrm { a } } } \text { is } \mathrm { p } ^ { \mathrm { a } } \mathrm { q } ^ { \mathrm { a } }$$

Question

Determine whether the statement is true or false.
-$$\text { If } \mathrm { a } > \mathrm { b } > \mathrm { c } \text {, then the greatest common factor of } \mathrm { p } ^ { \mathrm { a } } \mathrm { q } ^ { \mathrm { b } } , \mathrm { p } ^ { \mathrm { b } } \mathrm { q } ^ { \mathrm { c } } \text {, and } \mathrm { p } ^ { \mathrm { c } ^ { \mathrm { a } } } \text { is } \mathrm { p } ^ { \mathrm { a } } \mathrm { q } ^ { \mathrm { a } }$$

Quizplus · Accepted Answer

The greatest common factor (GCF) of $p^{a}q^{b}$, $p^{b}q^{c}$, and $p^{c^{a}}$ would be based on the lowest powers of $p$ and $q$ present in all terms, which are $p^c$ and $q^c$, not $p^a q^a$. The expression for $p^{c^a}$ seems to be a typo or misunderstanding; it doesn't align with the pattern of the other terms and doesn't affect the GCF based on the given $a > b > c$.

Determine Whether the Statement Is True or False