Mathematics, 24.06.2019 20:30 animelover730
What is the simplest form of 3 sqrt 27a^3b^7?
Answers: 1
![\sqrt[3]{27a^3b^7}\\\\\text{use}\ \sqrt[3]{xy}=\sqrt[3]{x}\cdot\sqrt[3]{y}\\\\=\sqrt[3]{27}\cdot\sqrt[3]{a^3}\cdot\sqrt[3]{b^7}=\sqrt[3]{3^3}\cdot\sqrt{a^3}\cdot\sqrt[3]{b^{3+3+1}}\\\\\text{use}\ \sqrt[3]{x^3}=x\ \text{and}\ a^n\cdot a^m=a^{n+m}\\\\=3\cdot a\cdot\sqrt[3]{b^3\cdot b^3\cdot b^1}\\\\\text{use}\ \sqrt[3]{xy}=\sqrt[3]{x}\cdot\sqrt[3]{y}\\\\=3a\cdot\sqrt[3]{b^3}\cdot\sqrt[3]{b^3}\cdot\sqrt[3]{b}\\\\\text{use}\ \sqrt[3]{x^3}=x\\\\=3a\cdot b\cdot b\cdot\sqrt[3]{b}=\boxed{3ab^2\sqrt[3]{b}}](/tpl/images/0013/0837/ce1e2.png)
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