Simplify the expression 8m^2n^2(2mn^3)^(1/3)

 Exercise

$8m^2n^2\sqrt[3]{6m^2n^5}.4m^2n^2\sqrt[3]{2mn^3}$

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The power of a product is equal to the product of it's factors raised to the same power

$8\sqrt[3]{2}m^2n^2\sqrt[3]{m}n$

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When multiplying exponents with same base we can add the exponents

$8\sqrt[3]{2}m^{\left(2+\frac{1}{3}\right)}n^2n$

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Simplify the addition $2+\frac{1}{3}$

$8\sqrt[3]{2}\sqrt[3]{m^{7}}n^2n$

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When multiplying exponents with same base you can add the exponents: $8\sqrt{m^{7}}n^2n$

$8\sqrt[3]{2}\sqrt[3]{m^{7}}n^{3}$

$8\sqrt[3]{2}\sqrt[3]{m^{7}}n^{3}$

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