Simplify the following expression without using a calculator:

${343}^{\frac{2}{3}}$

Write the following using exponents instead of the radicals:

${\left(\sqrt[4]{x}\right)}^3$

Write the following using exponents instead of the radicals:

${\left(\sqrt[4]{x}\right)}^3$

Write the following using exponents instead of the radicals:

${\left(\sqrt{x}\right)}^3$

Write the following using exponents instead of the radicals:

$\sqrt{x^5}$

Simplify. Where applicable, leave your final answer as a power of $x$.

${\left(x^{\frac{2}{3}}\right)}^2$

Simplify. Where applicable, leave your final answer as a power of $x$.

$x^{\frac{1}{3}}\times x^4$

Simplify. Where applicable, leave your final answer as a power of $x$.

$x^{\frac{1}{2}}\times x^{\frac{2}{3}}$

Simplify. Where applicable, leave your final answer as a power of $x$.

${\left(3^4\right)}^{\frac{1}{2}}$