32^(4/5) simplify?

Question

if you can do that, how do i do these three, as well??

2. 27^(5/3)
3. 16^(-1/4)


please show all these steps, i need to learn!
find x
5^x = 1 / 125

Answer 1

1. 5th root of 32 ^4=16

2. 3rd root of 27= 243

3.4th root ^-1= 1/2

4 5^x=1/125= 5^3=125 but since 1/125= 5^-3= 5 ^1/3

Answer 2

(FYI: since it sounds like your instructions were to SIMPLIFY and not to SOLVE, I'm showing you how to do that.)

Take the first example:

32^(4/5)

The key is to notice that the base number can also be represented as an exponential.

32 = 2^5

So, if you change that, now you have:

2^5^(4/5)

When you have something of the form x^A^B, it's the same as x^(A*B).

So, now you multiply 5*4/5, and you get 4.

So the answer is 2^4. Much simpler than 32^(4/5)

The other two have the same type of trick. To get you started on the next one, it's helpful to know that:

27=3^3

Then solve it the same way.

Answer 3

When you have a fraction as the exponent it is like taking the nth root of the denominator to the nth power of the numerator.

so your question would set up like this

fifth root of 32 to the fourth power. so do 32^4 and then take the fifth root of that number.

Answer 4

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