Answer
The solution of the given exponential expression is \[{{5}^{6}}\].
Work Step by Step
The quotient rule is defined as when an exponential is divided by another exponential expression of the same base, then subtract the exponent in the denominator from the exponent in the numerator and use this difference as the exponent of common base.
Let \[{{a}^{m}}\] and \[{{a}^{n}}\] be two exponential expressions, then \[\frac{{{a}^{m}}}{{{a}^{n}}}\] can be expressed as
\[\frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}}\]
In the same way, express the provided expression:
\[\begin{align}
& \frac{{{5}^{8}}}{{{5}^{2}}}={{5}^{8-2}} \\
& ={{5}^{6}}
\end{align}\]
Hence, the quotient rule for exponentials can be understood with the help of this example.
