please explain Perform the indicated operation and simplify

please explain

Perform the indicated operation and simplify. Assume all variables represent positive real numbers. squareroot 4 t^12 u^5 middot squareroot 28 t^7 u^10

Solution

sqrt(4t¹²u⁵) * sqrt(28 t⁷u¹⁰)

sqrt(4*28 t¹²u⁵t⁷u¹⁰) = sqrt(112t¹²⁺⁷u⁵⁺¹⁰)   =sqrt(112t¹⁹u¹⁵) = sqrt(112(t⁹)²*t* (u⁷)²*u)

                                                                                         = t⁹u⁷sqrt(4²*7tu) = 4t⁹u⁷sqrt(7 t u)