Solve left(9x^8y^3right)^1div2

$${ \left(9 { x }^{ 8 } { y }^{ 3 } \right) }^{ 1 \div 2 }$$

Evaluate

$$3\sqrt{y^{3}x^{8}}$$

Solution Steps

Expand \left(9x^{8}y^{3}\right)^{\frac{1}{2}}.

$$9^{\frac{1}{2}}\left(x^{8}\right)^{\frac{1}{2}}\left(y^{3}\right)^{\frac{1}{2}}$$

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

$$9^{\frac{1}{2}}x^{4}\left(y^{3}\right)^{\frac{1}{2}}$$

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

$$9^{\frac{1}{2}}x^{4}y^{\frac{3}{2}}$$

Calculate 9 to the power of \frac{1}{2} and get 3.

$$3x^{4}y^{\frac{3}{2}}$$

Differentiate w.r.t. x

$$12y^{\frac{3}{2}}x^{3}$$