Question

Multiply radicals. Help with #52

Answer 1

`\large\boxed{√(xy^3)\cdot\sqrt[3]{x^2y}=\sqrt[6]{x^7y^(11)}}`

Explanation:

`\text{Use}\ a^(1)/(n)=\sqrt[n]{a}\\\\√(xy^3)\cdot\sqrt[3]{x^2y}=(xy^3)^(1)/(2)(x^2y)^(1)/(3)\\\\\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^(nm)\\\\=x^(1)/(2)y^{(3)\left((1)/(2)\right)}x^{(2)\left((1)/(3)\right)}y^(1)/(3)\\\\\text{use}\ a^na^m=a^(n+m)\\\\=x^{(1)/(2)+(2)/(3)}y^{(3)/(2)+(1)/(3)}\\\\\text{the common denominator is 6}`

`(1)/(2)=(1\cdot3)/(2\cdot3)=(3)/(6)\\\\(2)/(3)=(2\cdot2)/(3\cdot2)=(4)/(6)\\\\(3)/(2)=(3\cdot3)/(2\cdot3)=(9)/(6)\\\\(1)/(3)=(1\cdot2)/(3\cdot2)=(2)/(6)\\\\x^{(1)/(2)+(2)/(3)}y^{(3)/(2)+(1)/(2)}=x^{(3)/(6)+(4)/(6)}y^{(9)/(6)+(2)/(6)}=x^{(7)/(6)}y^{(11)/(6)}=\sqrt[6]{x^7y^(11)}`