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

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Answer 1 · 2017-11-13T21:21:14

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

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:

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

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