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

Jun 7, 2016

$\frac{1}{\sqrt[3]{2} {x}^{3}}$

#### Explanation:

You only need to use three things:

• A negative exponent means the inverse of the positive exponent, so for example ${3}^{- 2} = \frac{1}{3} ^ 2$
• A rational exponent $\frac{m}{n}$ means that you have to take the $n$-th root of the $m$-th power, again as an example, ${4}^{\frac{5}{2}} = \sqrt{{4}^{5}}$
• 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

${x}^{- 5} / {x}^{- 2} = {x}^{- 5 + 2} = {x}^{- 3} = \frac{1}{x} ^ 3$

${2}^{\frac{1}{3}} = \sqrt[3]{2}$

And so, finally,

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