To simplify the expression 78x33

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