Which expression is equivalent to RootIndex 3 StartRoot 64 a Superscript 6 Baseline b Superscript 7 Baseline c Superscript 9 Baseline EndRoot?
2 a b c squared (RootIndex 3 StartRoot 4 a squared b cubed c EndRoot)
4 a squared b squared c cubed (RootIndex 3 StartRoot b EndRoot)
8 a cubed b cubed c Superscript 4 Baseline (RootIndex 3 StartRoot b c EndRoot)
8 a squared b squared c cubed (RootIndex 3 StartRoot b EndRoot)

Which expression is equal to ?

The correct answer is B.

Step-by-step explanation:

Inside of the radical you have . If you find the cube root of that, you get 4a^2. Go ahead and write that outside of the parenthesis:

If you re-write what is inside of the radical, you get:

Basically I expanded what was inside of the radical so I could find the cube roots of b^7 and c^9.

Now, take the cube root of b^7:

Notice how I could only factor out the two "b^3" that were inside the radical symbol, and how I left the b^1 inside the radical symbol because I couldn't factor it out.

Let's now get the cube root of c^9. Since it's a perfect cube, there won't be any "c"s left inside of the radical symbol:

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

step-by-step explanation: