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A number $x$ equals $2^{15}\cdot3^6$. What number's cube equals $x$?

 Feb 6, 2021
 #1
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\(\sqrt[3]{2^(15)* 3^6}\)   =  215/3 * 36/3  = 25 * 32

 Feb 6, 2021
 #2
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\(2^{15}\times3^6\rightarrow (2^5)^3 \times(3^2)^3\rightarrow (2^5\times 3^2)^3\)

 

so \(x^{1/3}=2^5\times3^2\)

 

which I'll leave you to simplify.

 Feb 6, 2021

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