Question

Simplify the following, using 2nd law, $a^{m} \div a^{n}=a^{m-n} : (\frac {5}{2})^8 \div (\frac {5}{2})^3$

Answer 1

5/2^(8-3)= 5/2^5 is the answer

Answer 2

Solution:

$a^{m} \div a^{n}=a^{m-n} \\ \\ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ \\ so \\ \\ (\frac {5}{2})^8 \div (\frac {5}{2})^3 \\ \\ = \frac{ { (\frac{5}{2}})^{8}} { { (\frac{5}{2} )}^{3} } \\ \\ since \: both \: the \: base \: are \: same \\ \\ = { (\frac{5}{2} })^{(8 - 3)} \\ \\ = {( \frac{5}{2} })^{5} \\ \\ = \frac{3125}{32}$
$a^{m} \div a^{n}=a^{m-n} : (\frac {5}{2})^8 \div (\frac {5}{2})^3 = { \frac{5}{2} }^{(8 - 3)}$

Hope it helps you.