Question

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

Answer 1

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