Solve (324b^4x^2)^1/2

$$( 324 b ^ { 4 } x ^ { 2 } ) ^ { 1 / 2 }$$

Evaluate

$$18|x|b^{2}$$

Solution Steps

Expand \left(324b^{4}x^{2}\right)^{\frac{1}{2}}.

$$324^{\frac{1}{2}}\left(b^{4}\right)^{\frac{1}{2}}\left(x^{2}\right)^{\frac{1}{2}}$$

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

$$324^{\frac{1}{2}}b^{2}\left(x^{2}\right)^{\frac{1}{2}}$$

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

$$324^{\frac{1}{2}}b^{2}x^{1}$$

Calculate 324 to the power of \frac{1}{2} and get 18.

$$18b^{2}x^{1}$$

Calculate x to the power of 1 and get x.

$$18b^{2}x$$

Differentiate w.r.t. x

$$18sign(x)b^{2}$$