Simplify \(1\times \sqrt{3\sqrt{3}}\) to \(\sqrt{3\sqrt{3}}\).
\[7+\sqrt{\sqrt{3\sqrt{3}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[7+{(3\sqrt{3})}^{\frac{1\times 1}{2\times 2}}\]
Simplify \(1\times 1\) to \(1\).
\[7+\sqrt[2\times 2]{3\sqrt{3}}\]
Simplify \(2\times 2\) to \(4\).
\[7+\sqrt[4]{3\sqrt{3}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[7+\sqrt[4]{3}\sqrt[4]{\sqrt{3}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[7+\sqrt[4]{3}\times {3}^{\frac{1\times 1}{2\times 4}}\]
Simplify \(1\times 1\) to \(1\).
\[7+\sqrt[4]{3}\sqrt[2\times 4]{3}\]
Simplify \(2\times 4\) to \(8\).
\[7+\sqrt[4]{3}\sqrt[8]{3}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[7+{3}^{\frac{3}{8}}\]
Decimal Form: 8.509804
7+3^(3/8)
