Question

Which expression is equivalent to (x^27y)^1/3?

A) x^3 (3√y)

B) x^9 (3√y)

C) x^27 (3√y)

D) x^24 (3√y)

Answer 1

Remember that (xᵃ. yᵇ)ⁿ = xᵃⁿ.yᵇⁿ

(x²⁷.y)¹/³ = x⁽²⁷ˣ¹/³⁾. y¹/³

x⁽²⁷ˣ¹/³⁾. y¹/³ =x⁸. y¹/³ = x⁹. ∛y. NONE OF THE ANSWERS, UNLESS YOU HAVE OMITTED SOMETHING, JUST AS 27 IS THE EXPONENT OF X AND ALSO ANOTHER 27 THAT MULTIPLIES Y??, In this case, it will be b

Answer 2

Option B).
`x^(9).(\sqrt[3]{y} )`.

Explanation:

The given expression is
`(x^(27)y)^{(1)/(3) }`.

We have to further simplify so that we can get the answer as shown in the options.

`(x^(27)y)^{(1)/(3) }=(x^(27))^{(1)/(3)}(y)^{(1)/(3)}`

[ As
`(x^(a).y^(b))^(m)=(x^(a))^(m).(y^(b))^(m)` ]

Now (
`(x^(27))^{(1)/(3)}(y)^{(1)/(3)}=(x^{(27)/(3) }).(y^{(1)/(3) } )=x^(9).(\sqrt[3]{y} )`

Therefore Option B. is the answer.