Solve {left(a^2b^6right)}^frac{1{2}}xleft(abright)^-1

$${ \left( { a }^{ 2 } { b }^{ 6 } \right) }^{ \frac{ 1 }{ 2 } } x { \left(ab \right) }^{ -1 }$$

Evaluate

$$\frac{x|a|\left(|b|\right)^{3}}{ab}$$

Solution Steps

Expand \left(a^{2}b^{6}\right)^{\frac{1}{2}}.

$$\left(a^{2}\right)^{\frac{1}{2}}\left(b^{6}\right)^{\frac{1}{2}}x\left(ab\right)^{-1}$$

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

$$a^{1}\left(b^{6}\right)^{\frac{1}{2}}x\left(ab\right)^{-1}$$

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

$$a^{1}b^{3}x\left(ab\right)^{-1}$$

Calculate a to the power of 1 and get a.

$$ab^{3}x\left(ab\right)^{-1}$$

Expand \left(ab\right)^{-1}.

$$ab^{3}xa^{-1}b^{-1}$$

Multiply a and a^{-1} to get 1.

$$b^{3}xb^{-1}$$

To multiply powers of the same base, add their exponents. Add 3 and -1 to get 2.

$$b^{2}x$$

Differentiate w.r.t. x

$$\frac{|a|\left(|b|\right)^{3}}{ab}$$