Question

5^4/5^7 simplified is

Answer 1

`(1)/(125)`

Explanation:

`1.apply \: exponent \: rules : \frac{ {x}^(a) }{ {x}^(b) } = {x}^(a - b)`

`= {5}^(4 - 7)`

`2.subtract \: the \: number : 4 - 7 = - 3`

`= {5}^( - 3)`

`3.apply \: exponent \: rule : {a}^( - b) = \frac{1}{ {a}^(b) }`

`= \frac{1}{ {5}^(3) }`

`4. \: {5}^(3) = 125`

`= (1)/(125)`

Answer 2

`\textbf{Given that,}\\\\~~~(5^4)/(5^7)\\\\\\=5^(4-7)~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Apply exponent rule:}~(a^m)/(a^n) = a^(m-n)\\\\\\=5^(-3)\\\\\\=\frac 1{5^3}~~~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Apply exponent rule:}~ a^(-n) = \frac 1 {a^n},~~~a \\eq 0 \\\\\\=\frac 1{125}\\\\\\=0.008`