Simplify `(7m-8n)^2+(7m+8n)^2`

Simplify (4m+5n)^2+(5m+4n)^2

Simplify (m^2-n^2m)^2+ 2m^3n^2

Simplify: 7^2 xx 2^2

Simplify (7^(1/2).8^(1/2))

Simplify: ((2^5)^2xx7^3)/(8^3xx7)

Simplify : (i) 2^(2/3)xx2^(1/5) (ii) (1/3^(3))^(7) (iii) 11^(1/2)/11^(1/4) (iv) 7^(1/2)*8^(1/2)

Prove that by using the principle of mathematical induction for all n in N : (2n+7) lt (n+3)^(2)

If cosec theta- sin theta = m and sec theta - cos theta = n , prove that: (m^(2)n)^(2/3)+(n^(2)m)^(2/3)=1 .