Question

Which expression is equivalent to 3/32x® y10 ? 4x27°(Vzx?y 2x*y$ (va 2x2y3 3 4xy 4x*y$ (32)

Answer 1

`3ab^2*\sqrt[3]{b}\text{ (option A)}`Step-by-step explanation:
`\sqrt[3]{27a^{^{}3}b^7}`

let's factorise in powers of 3 or in cube:

27 = 3³

b^7 = b^6 × b

b^6 = (b²)³

b^7 = (b²)³ × b

Then insert the above into the expression:

`\begin{gathered} \sqrt[3]{27a^{^{}3}b^7}\text{ =}\sqrt[3]{3^3* a^3*(b^2)^3* b} \\ =\text{ }\sqrt[3]{(3* a* b^2)^3}*\sqrt[3]{b}=3ab^2*\sqrt[3]{b} \\ =3ab^2*\sqrt[3]{b}\text{ (option A)} \end{gathered}`