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ollegr [7]
3 years ago
5

Find the simplified product:

Mathematics
2 answers:
ivann1987 [24]3 years ago
8 0
 I think we can do this by converting the radicals to exponents

the given expression =  2^1/3 * x^5/3 * 4 x^3
 = 4* 2^1/3 * x^14/3

the third option =  4 x^4 * 2^1/3  * x^2/3
                          = 4*2^1/3 * x^14/3 

so its the third option

Sunny_sXe [5.5K]3 years ago
4 0
Use:
\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{a\cdot b}\\\\a^n\cdot a^m=a^{n+m}\\\\(a^n)^m=a^{n\cdot m}\\\\\sqrt[n]{a^n}=a


\sqrt[3]{2x^5}\cdot\sqrt[3]{64x^9}=\sqrt[3]{2x^5}\cdot\sqrt[3]{64}\cdot\sqrt[3]{x^9}\\\\=\sqrt{2x^5}\cdot4\cdot\sqrt[3]{x^9}=4\sqrt[3]{2x^5\cdot x^9}\\\\=4\sqrt[3]{2x^{5+9}}=4\sqrt[3]{2x^{14}}=4\sqrt[3]{2x^{2+12}}=4\sqrt[3]{2x^2x^{12}}\\\\=4\sqrt[3]{2x^2x^{4\cdot3}}=4\sqrt[3]{2x^2(x^4)^3}=4\sqrt[3]{2x^2}\cdot\sqrt[3]{(x^4)^3}\\\\=4\sqrt[3]{2x^2}\cdot x^4=\boxed{4x^4\sqrt[3]{2x^2}}
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