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When you simplify \(\sqrt[3]{24a^4b^6c^{11}}\), what is the sum of the exponents of the variables that are outside the radical?

 

When you simplify $\sqrt[3]{24a^4b^6c^{11}}$, what is the sum of the exponents of the variables that are outside the radical?

 

I got 5 but it was wrong...

 Apr 21, 2019
 #1
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\sqrt[3]{24a^4b^6c^{11}}

 

\(\sqrt[3]{24a^4b^6c^{11}}\\ =\sqrt[3]{8*2*a^3*a*b^3*b^3*c^{9}*c^2}\\ =\sqrt[3]{2^3*a^3*b^3*b^3*c^{9}*2ac^2}\\ =2*a*b*b*c^3*\sqrt[3]{2ac^2}\\ =2ab^2c^3\sqrt[3]{2ac^2}\\ =2^1a^1b^2c^3\sqrt[3]{2ac^2}\\\)

 

The way I interprete the question the sum of the exponents of the variables that are outside the radical is 7

 

I expect you forgot the ones.    wink

 Apr 25, 2019

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