# How do you rewrite with fractional exponents for (root(4)(x))(3^4sqrt(x))?

May 27, 2015

$\sqrt[4]{x} = {x}^{\frac{1}{4}}$

$\sqrt{x} = {x}^{\frac{1}{2}}$

In general ${b}^{m} \cdot {b}^{n} = {b}^{m + n}$

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

$= {x}^{\frac{1}{4}} \cdot {3}^{4} \cdot {x}^{\frac{1}{2}}$

$= {3}^{4} {x}^{\frac{3}{4}}$