Question

simplify :-
5√x⁴4√x³3√x²√x

Expand:-
(-x/2+y+1/4)²

Answer 1

(1) Simplify:

$\sqrt[5]{ x^{4} } \sqrt[4]{ x^{3} } \sqrt[3]{ x^{2} } \sqrt{x} \\ \\ x^{ \frac{4}{5} } x^{ \frac{3}{4} } x^{ \frac{2}{3} } x^{ \frac{1}{2} } \\ \\ x^{( \frac{4}{5} + \frac{3}{4} + \frac{2}{3} + \frac{1}{2} )} \\ \\ x^{ \frac{48 + 45 + 40 + 30}{60} } \\ \\ x^{ \frac{163}{60} }$


(2) Exapand

Formula: $(a+b+c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca$

So,
$(- \frac{x}{2} + y + \frac{1}{4})^{2} = (- \frac{x}{2})^{2} + y^{2} + (\frac{1}{4})^{2} + 2(- \frac{x}{2})(y) + 2(y)( \frac{1}{4}) + 2(- \frac{x}{2})( \frac{1}{4}) \\ \\ = \frac{ x^{2} }{4} + y^{2} + \frac{1}{16} - xy + \frac{y}{2} - \frac{x}{4} \\ \\ \frac{ x^{2} }{4} + y^{2} - xy - \frac{x}{4} + \frac{y}{2} + \frac{1}{16}$