Solve (a^{-2/3}*b(a*b^{-2})^-frac{1{2}}(a^-1)^-frac{2{3}})^3=

$$( a ^ { - \frac { 2 } { 3 } } \cdot b ( a \cdot b ^ { - 2 } ) ^ { - \frac { 1 } { 2 } } ( a ^ { - 1 } ) ^ { - \frac { 2 } { 3 } } ) ^ { 3 } =$$

Evaluate

$$\frac{\left(b|b|\right)^{3}}{a^{\frac{3}{2}}}$$

Solution Steps

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

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

Multiply a^{-\frac{2}{3}} and a^{\frac{2}{3}} to get 1.

$$\left(b\left(ab^{-2}\right)^{-\frac{1}{2}}\right)^{3}$$

Expand \left(ab^{-2}\right)^{-\frac{1}{2}}.

$$\left(ba^{-\frac{1}{2}}\left(b^{-2}\right)^{-\frac{1}{2}}\right)^{3}$$

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

$$\left(ba^{-\frac{1}{2}}b^{1}\right)^{3}$$

Calculate b to the power of 1 and get b.

$$\left(ba^{-\frac{1}{2}}b\right)^{3}$$

Multiply b and b to get b^{2}.

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

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

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

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

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

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

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

Expand

$$\frac{\left(b|b|\right)^{3}}{a^{\frac{3}{2}}}$$

Solution Steps

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

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

Multiply a^{-\frac{2}{3}} and a^{\frac{2}{3}} to get 1.

$$\left(b\left(ab^{-2}\right)^{-\frac{1}{2}}\right)^{3}$$

Expand \left(ab^{-2}\right)^{-\frac{1}{2}}.

$$\left(ba^{-\frac{1}{2}}\left(b^{-2}\right)^{-\frac{1}{2}}\right)^{3}$$

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

$$\left(ba^{-\frac{1}{2}}b^{1}\right)^{3}$$

Calculate b to the power of 1 and get b.

$$\left(ba^{-\frac{1}{2}}b\right)^{3}$$

Multiply b and b to get b^{2}.

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

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

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

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

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

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

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