Question

If x is equal to a power n+m his equal to a power n+l z is equal to a power l+m then prove that x power multiply y power n multiply z powerl is equal to x power n multiply y is equal to land z is equal to m

Answer 1

X = am+n ", y = a ^ (n + 1) and z = 1+m al+, prove that

x ^ m * y ^ n * z ^ 1 = x ^ n * y ^ 1 * z ^ m

xmy¹z¹ =

= (am+n)m × (a¹+¹) × (a¹+m)¹

= am² +₁ +mn X a +In X a²²+ml

=

am² +m

+mn+n²+In+1² +ml

..(1)

Feedback

= (am+n) × (an+1)¹ × (al+m)m

=amn+n²

X alm+m²

= amn+n²+nl+1²+lm+m²

.(2)= (am+n)¹ × (an+¹)¹ × (a¹+m)m

= amn+n²

=an

X

X a

lm+m²

= amn+n²³+nl+1²+lm+m²

.(2)

comparing (1) and (2), its clear that,