Property 1 if `p/q ` is a rational number and m is a non -zero integer then `p/q = (p xx m) / ( q xx m )`

State whether the statements given are True or False. If (p)/(q) is a rational number and m is a non-zero integer, then (p)/(q) = (p xx m)/( q xx m)

State whether the statements given are True or False. If (p)/(q) is a rational number and m is a non-zero integer, then (p xx m)/( q xx m) is a rational number not equivalent to (p)/(q) .

Property 2 if p/q is a rational number and m is a common divisor of p and q then p/q=(p-:m)/(q-:m)

State whether the statements give are True or False. If (p)/(q) is a rational number and m is a non-zero common divisor of p and q, then (p)/(q) = (p div m)/( q div m)

If a is any real number and m;n are positive integers; then (a^p)^q = a^(pq) = (a^q)^p

If a is any real number and m;n are positive integers; then a^(p)xx a^(q)=a^(p+q)

If a is any real number and m;n are positive integers; then (a^(p))/(a^(q))=a^(p-q)

Generalisation : if a is a non - zero rational number and mnp are natural numbers then a^(m)xx a^(n)xx a^(p)=a^(m)+n+p

Is zero a rational number ? Can you write in the form p/q where p and q are integers and q ne 0 ?