Answer:
[tex]\displaystyle\mathsf{a^{10}}[/tex]
Step-by-step explanation:
Given the exponential expression, [tex]\displaystyle\mathsf{\frac{a^{15}}{a^{5}}}[/tex]:
We can use the Quotient Rule of Exponents, where it states that:
[tex]\displaystyle\mathsf{\frac{a^{m}}{a^{n}}\:=\:a^{(m\:-\:n)}}[/tex]
Since the exponential terms in numerator and the denominator both have the same base, a, we could simply subtract their exponents to simply the expression.
In other words:
[tex]\displaystyle\mathsf{\frac{a^{15}}{a^{5}}\:=\:a^{(15\:-\:5)}\:=\:a^{10}}[/tex]
Therefore, the simplified exponential expression is [tex]\displaystyle\mathsf{a^{10}}[/tex].
