Distribute fractional exponents

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January 26th 2013, 11:42 PM
ostheimerdl

Distribute fractional exponents

Please help with:

y^1/2(y^2/3+y^5/3)
January 27th 2013, 12:14 AM
earboth

Re: Distribute fractional exponents

Quote:

Originally Posted by ostheimerdl

Please help with:

y^1/2(y^2/3+y^5/3)

$y^{\frac12}\left(y^{\frac23} + y^{\frac53} \right) = y^{\frac12}\cdot y^{\frac23} + y^{\frac12}\cdot y^{\frac53}$

Now use the property of powers:

$b^a \cdot b^c = b^{a+c}$
January 27th 2013, 07:38 PM
Paze

Re: Distribute fractional exponents

Is this pre-calculus?
January 27th 2013, 08:01 PM
pspss

Re: Distribute fractional exponents

y^1/2(y^2/3 + y^5/3)
= y^1/2 × y^2/3 + y^1/2 × y^5/3)
= y^(1/2 + 2/3) + y^(1/2 + 5/3)
= y^(7/6) + y^(13/6)
= y^(7/6)[1 + y^(6/6)]
= y^(7/6)[1 + y^(1)]
= y^(7/6)[1 + y]
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