The equivalent expression is required.
The second option is correct 4a²b²c³(∛b)
Exponents
The given expression is [tex]\sqrt[3]{64a^6b^7c^9}[/tex]
The rules that will be used to solve the question are
[tex]\sqrt[n]{x}=x^{\dfrac{1}{n}}[/tex]
[tex]\sqrt[n]{xy}=\sqrt[n]{x}\sqrt[n]{y}=x^{\dfrac{1}{n}}y^{\dfrac{1}{n}}[/tex]
[tex]64=2\times 2\times 2\times 2\times 2\times 2=2^6[/tex]
So,
[tex]\sqrt[3]{64a^6b^7c^9}\\ =\sqrt[3]{2^6a^6b^7c^9}\\ =(2^6a^6b^6bc^9)^{\dfrac{1}{3}}\\ =2^{6\times \dfrac{1}{3}}\cdot a^{6\times \dfrac{1}{3}}\cdot b^{6\times \dfrac{1}{3}}\cdot b^{\dfrac{1}{3}}\cdot c^{9\times \dfrac{1}{3}}\\ =2^2a^2b^2\sqrt[3]{b}c^3\\ =4a^2b^2c^3(\sqrt[3]{b})[/tex]
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