Question

How do you simplify `x^-5 / (2^(1/3)x ^-2)`?

Answer 1

`1/(root(3)(2)x^3)`

Explanation:

You only need to use three things:

• A negative exponent means the inverse of the positive exponent, so for example `3^(-2)=1/3^2`
• A rational exponent `m/n` means that you have to take the `n`-th root of the `m`-th power, again as an example, `4^(5/2)=sqrt(4^5)`
• The ratio between two powers of the same base is a power whose exponent is the difference of the exponents, so `a^3/a^2=a^(3-2)=a`

Put those things together and you have

`x^{-5}/x^{-2}=x^{-5+2}=x^{-3}=1/x^3`

`2^{1/3}=root(3)(2)`

And so, finally,

# x^{-5}/(2^{-1/3}x^{-2})= 1/(root(3)(2)x^3) #