Solve (a^frac{1{2}}*b^-frac{4{3}})^3

$$( a ^ { \frac { 1 } { 2 } } \cdot b ^ { - \frac { 4 } { 3 } } ) ^ { 3 }$$

Evaluate

$$\frac{a^{\frac{3}{2}}}{b^{4}}$$

Solution Steps

Expand \left(a^{\frac{1}{2}}b^{-\frac{4}{3}}\right)^{3}.

$$\left(a^{\frac{1}{2}}\right)^{3}\left(b^{-\frac{4}{3}}\right)^{3}$$

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

$$a^{\frac{3}{2}}\left(b^{-\frac{4}{3}}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{4}{3} and 3 to get -4.

$$a^{\frac{3}{2}}b^{-4}$$

Expand

$$\frac{a^{\frac{3}{2}}}{b^{4}}$$

Solution Steps

Expand \left(a^{\frac{1}{2}}b^{-\frac{4}{3}}\right)^{3}.

$$\left(a^{\frac{1}{2}}\right)^{3}\left(b^{-\frac{4}{3}}\right)^{3}$$

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

$$a^{\frac{3}{2}}\left(b^{-\frac{4}{3}}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{4}{3} and 3 to get -4.

$$a^{\frac{3}{2}}b^{-4}$$