Solve (25x^4y^6)^frac{1{2}}

$$( 25 x ^ { 4 } y ^ { 6 } ) ^ { \frac { 1 } { 2 } }$$

Evaluate

$$5x^{2}\left(|y|\right)^{3}$$

Solution Steps

Expand \left(25x^{4}y^{6}\right)^{\frac{1}{2}}.

$$25^{\frac{1}{2}}\left(x^{4}\right)^{\frac{1}{2}}\left(y^{6}\right)^{\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and \frac{1}{2} to get 2.

$$25^{\frac{1}{2}}x^{2}\left(y^{6}\right)^{\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and \frac{1}{2} to get 3.

$$25^{\frac{1}{2}}x^{2}y^{3}$$

Calculate 25 to the power of \frac{1}{2} and get 5.

$$5x^{2}y^{3}$$

Differentiate w.r.t. x

$$10x\left(|y|\right)^{3}$$