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

1 Answer
Nov 13, 2017

Answer:

#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)#