Final Answer
$\sqrt[5]{x^2-2}\sqrt[3]{x^{4}}+4\sqrt[5]{x^2-2}x^2+4\sqrt[5]{x^2-2}x+\sqrt[5]{x^2-2}+4\sqrt[3]{x^{5}}\sqrt[5]{x^2-2}+2\sqrt[5]{x^2-2}\sqrt[3]{x^{2}}$
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Step-by-step Solution
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1
Simplify $\sqrt[3]{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{3}$
$\left(\sqrt[3]{x^{2}}+2x+1\right)^2\sqrt[5]{x^2-2}$
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$\left(\sqrt[3]{x^{2}}+2x+1\right)^2\sqrt[5]{x^2-2}$
Learn how to solve problems step by step online. Expand the expression (x^2^1/3+2x+1)^2(x^2-2)^1/5. Simplify \sqrt[3]{x^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{3}. Expand \left(\sqrt[3]{x^{2}}+2x+1\right)^2. Expand \left(2x+1\right)^2. The power of a product is equal to the product of it's factors raised to the same power.
Final Answer
$\sqrt[5]{x^2-2}\sqrt[3]{x^{4}}+4\sqrt[5]{x^2-2}x^2+4\sqrt[5]{x^2-2}x+\sqrt[5]{x^2-2}+4\sqrt[3]{x^{5}}\sqrt[5]{x^2-2}+2\sqrt[5]{x^2-2}\sqrt[3]{x^{2}}$