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\(2\sqrt{\sqrt{x}}\cdot 2\sqrt{x}\)

First, we change to fractional exponents:

\(2\left(x^{\frac{1}{2}}\right)^{\frac{1}{2}}\cdot 2\left(x\right)^{\frac{1}{2}}\)

Multiply the 2's

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

Use exponent laws to multiple a power to a power

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

Now add the exponents using the product rule for laws of exponents

\(4\left(x^{\frac{1}{4}+\frac{1}{2}}\right)=4\left(x\right)^{\frac{3}{4}}\)

Bring back to radical form:

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

Your answer :)

Great