Question

HELP PLEASE SIMPLIFY !!!

Answer 1

`=x^{(5)/(6)}+2x^{(7)/(3)}`

Explanation:

`x^{(1)/(3)}\left(x^{(1)/(2)}+2x^2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=x^{(1)/(3)},\:b=x^{(1)/(2)},\:c=2x^2\\=x^{(1)/(3)}x^{(1)/(2)}+x^{(1)/(3)}\cdot \:2x^2\\=x^{(1)/(3)}x^{(1)/(2)}+2x^2x^{(1)/(3)}\\\mathrm{Simplify}\:x^{(1)/(3)}x^{(1)/(2)}+2x^2x^{(1)/(3)}:\quad x^{(5)/(6)}+2x^{(7)/(3)}\\x^{(1)/(3)}x^{(1)/(2)}+2x^2x^{(1)/(3)}\\x^{(1)/(3)}x^{(1)/(2)}=x^{(5)/(6)}`

`x^{(1)/(3)}x^{(1)/(2)}\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)\\x^{(1)/(3)}x^{(1)/(2)}=\:x^{(1)/(3)+(1)/(2)}\\=x^{(1)/(3)+(1)/(2)}\\\mathrm{Join}\:(1)/(3)+(1)/(2):\quad (5)/(6)\\(1)/(3)+(1)/(2)\\\mathrm{Least\:Common\:Multiplier\:of\:}3,\:2:\quad 6\\Adjust\:Fractions\:based\:on\:the\:LCM\\=(2)/(6)+(3)/(6)`

`\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad (a)/(c)\pm (b)/(c)=(a\pm \:b)/(c)\\=(2+3)/(6)\\\mathrm{Add\:the\:numbers:}\:2+3=5\\=(5)/(6)\\=x^{(5)/(6)}\\2x^2x^{(1)/(3)}=2x^{(7)/(3)}\\=x^{(5)/(6)}+2x^{(7)/(3)}`