$\sqrt[4]{{x}^{4+1}}$
Use ${a}^{m+n}={a}^{m} \times {a}^{n}$ to expand the expression$\sqrt[4]{{x}^{4} \times {x}^{1}}$
Any expression raised to the power of $1$ equals itself$\sqrt[4]{{x}^{4} \times x}$
The root of a product is equal to the product of the roots of each factor$\sqrt[4]{{x}^{4}}\sqrt[4]{x}$
Reduce the index of the radical and exponent with $4$$x\sqrt[4]{x}$