Question

How do you fully simplify `sqrt(x^15y^9)`?

Answer 1

`x^7.5y^4.5` OR EQUIVALENTLY `x^7y^4sqrt(xy)`

Explanation:

Start by rewriting the square root in an equivalent exponent form:

`sqrt(x^15y^9)=(x^15y^9)^(1/2)`

Use the power rule:

`(x^15y^9)^(1/2)=x^7.5y^4.5`

This could be considered simplest form, but if you did not want fractions in the exponents, you could rewrite this using the product rule:

`=x^7x^0.5y^4y^0.5=x^7sqrt(x)y^4sqrt(y)=x^7y^4sqrt(xy)`