Simplify Write with positive exponents Assume that all varia

Simplify. Write with positive exponents. Assume that all variables represent positive real numbers. p^1/9 p^11/18 p^1/2/(p^16)^-1/9 p^1/9 p^11/18 p^1/2/(p^16)^-1/9 = (Simplify your answer. Type exponential notation with positive exponents.)

Solution

We have (p^1/9p^11/18 p^1/2)/ (p¹⁶)^-1/9 = (p^1/9+1/18+1/2)/p^-16/9 ( as x^m xⁿ = x^m+n and (x^m)ⁿ = x^mn )

= (p ^22/18)(p^16/9) (as 1/x^-m = x^m)

= p ^22/18+16/9= p ^54/18 = p³. The answer is p³.