Question

Which property of exponents must be used first to solve this expression? (xy^2)^1/3

Answer 1

(ab)n=anbn......................................

Answer 2

The required property of exponent is power of a product property, i.e.,
`(ab)^n=a^nb^n`.

Explanation:

The given expression is

`(xy^2)^{(1)/(3)}`

To simplify this expression the first property of exponents which is used , is the power of a product property.

According to the power of a product property of exponents

`(ab)^n=a^nb^n`

Using this property the given expression can be written as

`(xy^2)^{(1)/(3)}=x^{(1)/(3)}(y^2)^{(1)/(3)}`

Therefore the required property of exponent is power of a product property, i.e.,
`(ab)^n=a^nb^n`.