1. ## Fractional Indices

$\displaystyle 4n^{3/2} = 8^{-1/3}$

Find the value of n

hi all, ive been given the above and need to solve it without a calculator. ive expessed it in all the indice rules but cant come up with a suitable format to solve it.

any ideas?

here's what i got so far $\displaystyle n^{3/2} = \frac{1}{8}$
so does $\displaystyle n = \sqrt[{3/2}]{1/8}$

$\displaystyle (n^{3/2})^{2/3}=(2^{-3})^{2/3}$
therefore
$\displaystyle n=2^{-2}$
therefore
$\displaystyle n=\frac{1}{2^2}$

2. Welcome to the Forum

$\displaystyle 4 = 2^2$

$\displaystyle 8 = 2^3$

using it in
$\displaystyle 4n^{3/2} = 8^{-1/3}$

we get
$\displaystyle 2^2 n^{3/2} = (2^{3})^{-1/3}$

divide both sides by 2^2

$\displaystyle n^{3/2} = \frac {2^{-1} }{2^2}$

Thus
$\displaystyle n^{3/2} = 2^{-1 - 2}$

Hence

$\displaystyle n^{3/2} = 2^{-3}$

This can be written as

$\displaystyle (n^{3/2})^{2/3} = (2^{-3})^{2/3}$

Hence

$\displaystyle n^1 = \frac{1}{2^{(2*3)/3}}$

Hence $\displaystyle n= \frac{1}{4}$

3. wow thanks for taking the time to look at that one. i thought id covered them all except i didnt think about converting 2 to the power of n as a first step. and multiplying by the reciprocal.

now i can do it without a calculator

thanks for the welcome too. how can you format questions like your answer, ie using mathematical symbols?

4. Its really good that you have asked about it ...Inorder to format