SOLUTION: I am so lost with no hope of finding daylight on this one. Can someone break this down so that is easier to understand? What expression raised to the fourth power is 81x^12y^8z^

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am so lost with no hope of finding daylight on this one. Can someone break this down so that is easier to understand? What expression raised to the fourth power is 81x^12y^8z^      Log On


   

Question 88117: I am so lost with no hope of finding daylight on this one. Can someone break this down so that is easier to understand?
What expression raised to the fourth power is 81x^12y^8z^16?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


I am so lost with no hope of finding daylight on this one. 

Can someone break this down so that is easier to understand?

What expression raised to the fourth power is 81x^12y^8z^16



Let the answer be w



So 



w%5E4 = 81x%5E12y%5E8z%5E16



Raise both sides to the 1/4 power, which is the same as

fourth root and there are always 2 even roots of every

number but 0, one positive and one negative: 



%28w%5E4%29%5E%281%2F4%29 = ±%2881x%5E12y%5E8z%5E16%29%5E%281%2F4%29



Write 81 as 3%5E4



w = ±%283%5E4x%5E12y%5E8z%5E16%29%5E%281%2F4%29



Multiply each inner exponent on the right by the outer exponent 1%2F4



w = ±3%5E%284%281%2F4%29%29x%5E%2812%281%2F4%29%29y%5E%288%281%2F4%29%29z%5E%2816%281%2F4%29%29



w = ±3%5E1x%5E3y%5E2z%5E4



w = ±3x%5E3y%5E2z%5E4



Edwin