# To simplify the expression \sqrt[3]{\frac{7}{8x^{3}}}

To simplify the expression $\sqrt[3]{\frac{7}{8{x}^{3}}}$

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Calculation:
According to quotient property of square root $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$
And the product property of square root states $\sqrt{ab}=\sqrt{a}\cdot \sqrt{b}$.
Given expression is $\sqrt[3]{\frac{7}{8{x}^{3}}}$
This can be written as $\sqrt[3]{\frac{7}{8{x}^{3}}}=\sqrt[3]{\frac{7}{2×2×2×{x}^{3}}}$
$\sqrt[3]{\frac{7}{8{x}^{3}}}=\sqrt[3]{\frac{7}{2×2×2×{x}^{3}}}$
Applying the quotient rule,
$\sqrt[3]{\frac{7}{8{x}^{3}}}=\frac{\sqrt[3]{7}}{\sqrt[3]{2×2×2×{x}^{3}}}$
Applying the product rule for Denominator,
$\sqrt[3]{\frac{7}{8{x}^{3}}}=\frac{\sqrt[3]{7}}{\sqrt[3]{\left(2{\right)}^{3}×\sqrt[3]{{x}^{3}}}}$
$\sqrt[3]{\frac{7}{8{x}^{3}}}=\frac{\sqrt[3]{7}}{2x}$