Frank Day

2022-07-06

Simple Fraction needing explanation
$\frac{x}{{x}^{-1/2}}={x}^{3/2}$
How? I don't see what is going on here. What rule is being used to achieve this amount?

Tristin Case

Expert

Use
$\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}$
so
$\frac{x}{{x}^{-1/2}}=\frac{{x}^{1}}{{x}^{-1/2}}={x}^{1-\left(-1/2\right)}={x}^{3/2}$

aangenaamyj

Expert

Use: ${x}^{a}{x}^{b}={x}^{a+b}$
$\frac{x}{{x}^{-1/2}}=\frac{x}{{x}^{-1/2}}\frac{{x}^{1/2}}{{x}^{1/2}}=\frac{x\cdot {x}^{1/2}}{1}={x}^{1+1/2}={x}^{3/2}$

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