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Simplify $\sqrt[8]{a^7}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $7$ and $n$ equals $\frac{1}{8}$
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$\left(\sqrt[8]{a}-\sqrt[4]{12}\right)\left(\sqrt[8]{a^{7}}+\sqrt[4]{12^3}\right)$
Learn how to solve polynomial factorization problems step by step online. Expand the expression (a^(1/8)-12^(1/4))(a^7^(1/8)+12^3^(1/4)). Simplify \sqrt[8]{a^7} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 7 and n equals \frac{1}{8}. Simplify \sqrt[4]{12^3} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals \frac{1}{4}. Multiply the single term \sqrt[8]{a^{7}}+\sqrt[4]{\left(12\right)^{3}} by each term of the polynomial \left(\sqrt[8]{a}-\sqrt[4]{12}\right). Multiply the single term -\sqrt[4]{12} by each term of the polynomial \left(\sqrt[8]{a^{7}}+\sqrt[4]{\left(12\right)^{3}}\right).