Answered

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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

Sagot :

[tex]\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[/tex]
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