Given xgt 0 rewrite the following expression in simplest form. sqrt (81x^10)cdot sqrt [4](256x^8) Answer Allemptiout of 2 square

To simplify the given expression, we need to rewrite it in terms of fractional exponents and then combine the terms.<br /><br />Given expression:<br />$\sqrt {81x^{10}}\cdot \sqrt [4]{256x^{8}}$<br /><br />Step 1: Rewrite the square root and fourth root in terms of fractional exponents.<br />$\sqrt {81x^{10}} = (81x^{10})^{1/2}$<br />$\sqrt [4]{256x^{8}} = (256x})^{1/4}$<br /><br />Step 2: Simplify the exponents.<br />$(81x^{10})^{1/2} = 9x^{5}$<br />$(256x^{8})^{1/4} = 4x^{2}$<br /><br />Step 3: Multiply the simplified terms.<br />$9x^{5} \cdot 4x^{2} = 36x^{7}$<br /><br />Therefore, the simplified form of the given expression is:<br />$\boxed{36x^{7}}$