Question

Show me how you solve it

Answer 1

5^20

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 * 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 * 4) } \\ \displaystyle \large{( \frac{ {5}^(8) }{ {5}^(3) } )^(4) = {5}^(20) }`