Question

write the law of exponents in case of rational numbers

Answer 1

For any rational number
$\frac{a {}^{n} }{a {}^{m} } = {a}^{n - m}$
${a}^{n} \times {a}^{m} = {a}^{n + m}$
$(a \times b) {}^{n} \\ = {a}^{n} \times {b}^{n}$
${a}^{n} \times {b}^{n} = (a \times b) {}^{n}$
$(a {}^{n} ) {}^{m} = {a}^{mn}$