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The Multiplication Property of Square Roots tells us that sqrt(ab)=sqrt(a) * sqrt(b), for a≥ 0 and b≥ 0.
-2sqrt(a)/a^2
We want to simplify a radical expression.
To do so we will assume that a>0, otherwise the given expression would not be defined.
-2/sqrt(a^3)
Let's recall the Multiplication Property of Square Roots.
Split into factors
sqrt(a* b)=sqrt(a)*sqrt(b)
sqrt(a^2)=a
Now that we have simplified the factors as much as possible, we need to rationalize the denominator. To do this, we will multiply the numerator and denominator by a square root that will eliminate the radical in the denominator.
a/b=a * sqrt(a)/b * sqrt(a)
sqrt(a)* sqrt(a)= a
a* a=a^2