write the expression in simplest form.....three divided by the 5th square root of 16?

Question

by the 5th square root of 16 i mean there is a little 5 in front of the square root sign

the problem would be 3/(16^1/5)

Answer 1

3/2*(2^1/5) *note this is the simplest form and your solution*

you can multiple the bottom and top by 16^4/5. Once you have that, you will have (3*16^4/5)/16.

You can expand 16^4/5 to 32768^1/5 * 2^1/5.
32768^1/5 = 8
8*3 = 24/16 = 3/2 then you have 2^1/5 leftover
so it is 3/2 * 2^1/5 = 1.723

Both users above have responses that do not compute to 1.723 (the intended solution to your problem)

Answer 2

5th root of 16 means 5 of them multiplied together equal 16. since you already have 1 of them on the bottom, multiply top and bottom by 4 of them. that puts a nice 16 on the bottom, and 3 times 5th root of 16^4 on top. since 16 is 2^4, 16^4 = 2^16. 5th root of that is (dividing 16 by 5) 2^3 times 5th root of 16. that makes top 3•8• 5th root of 16, and 16 on the bottom. the 8/16 part simplifies to 2 on the bottom, so you end up with 3/2 times 5th root of 16.

Answer 3

put the exponent 5 over the whole thing and distribute


243
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16