Solve (a^2b^frac{1{2}})^-3x(ab^frac{5{2}})

$$( a ^ { 2 } b ^ { \frac { 1 } { 2 } } ) ^ { - 3 } x ( a b ^ { \frac { 5 } { 2 } } )$$

Evaluate

$$\frac{bx}{a^{5}}$$

Solution Steps

Expand \left(a^{2}b^{\frac{1}{2}}\right)^{-3}.

$$\left(a^{2}\right)^{-3}\left(b^{\frac{1}{2}}\right)^{-3}xab^{\frac{5}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$a^{-6}\left(b^{\frac{1}{2}}\right)^{-3}xab^{\frac{5}{2}}$$

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

$$a^{-6}b^{-\frac{3}{2}}xab^{\frac{5}{2}}$$

To multiply powers of the same base, add their exponents. Add -6 and 1 to get -5.

$$a^{-5}b^{-\frac{3}{2}}xb^{\frac{5}{2}}$$

To multiply powers of the same base, add their exponents. Add -\frac{3}{2} and \frac{5}{2} to get 1.

$$a^{-5}b^{1}x$$

Calculate b to the power of 1 and get b.

$$a^{-5}bx$$

Differentiate w.r.t. x

$$\frac{b}{a^{5}}$$