How would i even begin to simplify this?

Question

[(x^2 -36)^4] / (divided by) [(x^2 -12x+36) (times) sqrt(x+6)]

__________ divided by ___________________________

t h i s t h i s w h o l e o t h e r o n e

Answer 1

Please see video. :-)

Answer 2

[(x² - 36)⁴] / [(x² - 12x + 36)√(x+6)]

Let's start factoring each individual expressions.

[(x - 6)(x + 6)]⁴ / [(x - 6)² √(x+6)]

Use the Power Property of Exponents

(x - 6)⁴(x + 6)⁴ / (x - 6)²(x+6)^1/2

Use the Quotient Property of Exponents.

(x - 6)^4-2(x + 6)^4-(1/2) = (x - 6)²(x + 6)^3/2 or (x - 6)²√(x + 6)³