Concept:Use laws of indices to simplify the product of powers.Explanation:We are given:a=xym−1b=xyn−1c=xyp−1Compute an−pbp−mcm−n.Step 1: Substitute and apply power rule (uv)r=urvr:an−p=(xym−1)n−p=xn−py(m−1)(n−p)bp−m=(xyn−1)p−m=xp−my(n−1)(p−m)cm−n=(xyp−1)m−n=xm−ny(p−1)(m−n)Step 2: Multiply the x powers:xn−p⋅xp−m⋅xm−n=x(n−p)+(p−m)+(m−n)=x0=1Step 3: Multiply the y powers:Exponent sum =(m−1)(n−p)+(n−1)(p−m)+(p−1)(m−n)Expand each term:(m−1)(n−p)=mn−mp−n+p(n−1)(p−m)=np−nm−p+m(p−1)(m−n)=pm−pn−m+nAdd them: mn−mp−n+p+np−nm−p+m+pm−pn−m+nAll terms cancel: mn−nm=0, −mp+pm=0, np−pn=0, −n+n=0, p−p=0, m−m=0Thus y0=1.Step 4: Total product =1×1=1.Answer:1