Question

find the value of n: 5^10÷5^8=(1/5)n

Answer 1

ʜᴇʟʟᴏ ᴍᴀᴛᴇ!

5^10 / 5^8 = ( 1/5 )^n

a^m ÷ a^n = a^( m - n )

5^( 10 - 8 ) = 5^-n

5^2 = 5^-n

On comparing two side we get,

2 = - n or n = - 2

Or

If you meant to 5^10 ÷ 5^8 = (1/5)n
Then,
5^2 = n/5
25 × 5 = n and n = 125

Hope it helps

Answer 2

$\frac{ {5}^{10} }{ {5}^{8} } = (\frac{1}{5} ) ^{n} \\ \\ \\ = > {5}^{10 - 8} = {5}^{ - n} \\ \\ \\ => {5}^{2} = {5}^{ - n}$


If bases are equal, powers are also equal,


=> 2 = -n

=> -2 = n