Question

Anyone help me. ....​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the rules of exponents

All the exponents inside the parenthesis are multiplied by the exponent outside the parenthesis.

Then

$\frac{m^{-7}n^{14} }{m^{-25}n^{40} }$ ÷ $\frac{m^{-21}n^{42} }{m^{-25}n^{40} }$

[ Using the rule $\frac{a^{m} }{a^{n} }$ = $a^{(m-n)}$ ]

= $m^{(-7-14)}$ $n^{(14-(-28)}$ ÷ $m^{(-15-10)}$ $n^{(25-(-15)}$

= $m^{-21}$ $n^{14+28}$ ÷ $m^{-25}$ $n^{25+15}$

= $\frac{m^{-21}n^{42} }{m^{-25}n^{40} }$

= $m^{(-21-(-25))}$ $n^{(42-40)}$

= $m^{(-21+25)}$ n²

= $m^{4}$ n² = $m^{x}$ $n^{y}$ , so x = 4 and y = 2

Then

$m^{x-2y}$ = $m^{4-2(2)}$ = $m^{4-4}$ = $m^{0}$ = 1 ← as required