Question

Which expression is equivalent to (x27y)^1/3

Answer 1

3∛(xy)

Explanation:

(x27y)^1/3

Simplified form will be 3/x³y³

Because;

27^(1/3) = 3

x^(1/3) = ∛x

y^(1/3) = ∛y

Which gives us 3∛(xy)

Answer 2

`(x^(9)y^(1)/(3))`

or

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

Explanation:

Given in the question an expression

`(x^(27)y )^(1)/(3)`

We will apply the power rule

The "power rule" tells us that to raise a power to a power, just multiply the exponents.

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

`(x^(9)y^(1)/(3))`

As we know that

`x^(1/n) = \sqrt[n]{x}`

so we can write the above expression as

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