Question

Show me how you solve it

Answer 1

Answer:

5^20

Step-by-step explanation:

Law of Exponent I

$\displaystyle \large{ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

Therefore:

$\displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = ({5}^{8 - 3})^{4} } \\ \displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = ({5}^{5})^{4} }$

Law of Exponent II

$\displaystyle \large{( {a}^{m} ) ^{n} = {a}^{m \times n} }$

Thus:

$\displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = ({5}^{8 - 3})^{4} } \\ \displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = ({5}^{5})^{4} } \\ \displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = {5}^{5 \times 4} } \\ \displaystyle \large{( \frac{ {5}^{8} }{ {5}^{3} } )^{4} = {5}^{20} }$