Answer:
5^20
Step-by-step explanation:
Law of Exponent I
[tex] \displaystyle \large{ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }[/tex]
Therefore:
[tex] \displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = ({5}^{8 - 3})^{4} } \\ \displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = ({5}^{5})^{4} }[/tex]
Law of Exponent II
[tex] \displaystyle \large{( {a}^{m} ) ^{n} = {a}^{m \times n} }[/tex]
Thus:
[tex] \displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = ({5}^{8 - 3})^{4} } \\ \displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = ({5}^{5})^{4} } \\ \displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = {5}^{5 \times 4} } \\ \displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = {5}^{20} }[/tex]
