Question

The number 32 to the power of 1 over 5 is equal to 2. Explain why this is so, what does it mean when a number has a fractional index? Write this number without using an index

Answer 1

When you have a power of a fraction, say 1/n, it is the same as this:

\[a ^{1/n} = \sqrt[n]{a}\]

Answer 2

" a to the power of 1/n, is the same as the nth root of a"

Answer 3

what does that tell you about 32 to the 1/5th power?

Answer 4

\[\sqrt[5]{32}\] ?

Answer 5

correct,

that is the same as, "what number multiplied to itself 5 times is 32"

n x n x n x n x n = 32?

Answer 6

which is 6.4 right?

Answer 7

@raphaelll - you have worked out a number that, when multiplied by 5, will give 32. i.e. \(6.4\times5=32\)

what @DanJS was asking you is what number, when multiplied by ITSELF 5 times, will give you 32.

e.g. 3 multiplied by itself 5 times will give you: \(3\times3\times3\times3\times3=243\)

Answer 8

Right, so this discussion was an explanation to answer the question.

Answer 9

2 to the 5th power = 5 *5*5*5*5 = 32
and
\[32 ^{1/5} = \sqrt[5]{32} = 2\]

Answer 10

Oh I see! That makes so much sense, thanks guys