b) 16^x = 32. Now 2^4 = 16, while 2^5 = 32. So we need (2^4)^x = 2^5, and so 4x = 5, and x = 5/4. Thus 16^(5/4) = 32

a^1/3 = .3

(a^1/3)^3 = a, so a = .3^3. Use this technique on b and c

lets start with the power of 2 for 64

64=2×32 or

2x2x16 or

2x2x2x8 hopefully you see where this is going =D

64=2 x 2 x 2 x 2 x 2 x 2

so then you add up your 2s and you’re left with 2^6

now for the power of 4

64=4 x 4 x 4

and then add up your 4s and have 4^3

now 16 is a little more difficult because it won’t come out nice

knowing that 64=16×8

so 8 is half of 16 so we can look at it like 64=16x(.5×16) so if you add up the 16s you would have 1.5

so 16^1.5

then you can do the same thing with 32

32= 2 x 2 x 2 x 2 x 2

32= 4 x 4 x (.5×4)

and then power of fractions is a totally different beast

because if you try to multiply .5 x .5 and so on the numbers are going to keep getting smaller so you’ll have to look at it differently. you can rewrite 1/x^n as x^-n so it will be the the negative version of the power of 2 or 1/2^-5

hope this helps

the first power of 2 is 2

the second power of 2 is 2 x 2

the third power of 2 is 2 x 2 x 2

The arithmetic is straightforward for integers.

For vulgar fractions think of using reciprocals, usually expressed as negative numbers.

(It’s a long time since I had to do these.)