Question

Which of the following expressions does not equal: the sixth root of 81x^4y^8

a. (3xy^2)^2/3

b. (3x)^2/3y^4/3

c. (3x^2y^4)^1/3

d. cube root of 9x^2y^4

Answer 1

`\sqrt[6]{81x^4y^8}=\left[3^4x^4(y^2)^4\right]^(1)/(6)=\left[\left(3xy^2\right)^4\right]^(1)/(6)\\\\=\left(3xy^2\right)^{4\cdot(1)/(6)}=\left(3xy^2\right)^(2)/(3)\to A\\\\=\left(3xy^2\right)^(2)/(3)=\sqrt[3]{\left(3xy^2\right)^2}=\sqrt[3]{9x^2y^4}\to D\\\\=\left(3xy^2\right)^(2)/(3)=\left(3x\right)^(2)/(3)y^{2\cdot(2)/(3)}=\left(3x\right)^(2)/(3)y^(4)/(3)\to B\\\\\\Answer:C`