Solve (25x^10y^8)^1/2

$$( 25 x ^ { 10 } y ^ { 8 } ) ^ { 1 / 2 }$$

Evaluate

$$5y^{4}\left(|x|\right)^{5}$$

Solution Steps

Expand \left(25x^{10}y^{8}\right)^{\frac{1}{2}}.

$$25^{\frac{1}{2}}\left(x^{10}\right)^{\frac{1}{2}}\left(y^{8}\right)^{\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and \frac{1}{2} to get 5.

$$25^{\frac{1}{2}}x^{5}\left(y^{8}\right)^{\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and \frac{1}{2} to get 4.

$$25^{\frac{1}{2}}x^{5}y^{4}$$

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

$$5x^{5}y^{4}$$

Differentiate w.r.t. x

$$25|x|x^{3}y^{4}$$