Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Simplify and leave in radical form.

4√(xy³)

Step-by-step explanation:

8√(x²y⁶)

The above expression can be simplified as follow:

8√(x²y⁶)

Recall:

m√a = a^1/m

Therefore,

8√(x²y⁶) = (x²y⁶)^1/8

Recall:

(aⁿ)^1/m = a^(n/m)

Therefore,

(x²y⁶)^1/8 = x^(2/8)•y^(6/8)

= x^1/4•y^3/4

= (xy³)^1/4

Recall :

a^1/m = m√a

Therefore,

(xy³)^1/4 = 4√(xy³)

Therefore,

8√(x²y⁶) = 4√(xy³)

x=30

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4