Solve {left(a^2b^4right)}^frac{1{4}}

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

Evaluate

$$\sqrt{|a|}|b|$$

Solution Steps

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

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

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

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

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

$$a^{\frac{1}{2}}b^{1}$$

Calculate b to the power of 1 and get b.

$$a^{\frac{1}{2}}b$$

Differentiate w.r.t. a

$$\frac{|b|sign(a)}{2\sqrt{|a|}}$$