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

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

Evaluate

$$\left(\frac{b}{a}\right)^{\frac{14}{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and -\frac{4}{3} to get -\frac{7}{3}.

$$\left(a^{-\frac{7}{3}}b^{\frac{1}{3}}b^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add \frac{1}{3} and 2 to get \frac{7}{3}.

$$\left(a^{-\frac{7}{3}}b^{\frac{7}{3}}\right)^{2}$$

Expand \left(a^{-\frac{7}{3}}b^{\frac{7}{3}}\right)^{2}.

$$\left(a^{-\frac{7}{3}}\right)^{2}\left(b^{\frac{7}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{7}{3} and 2 to get -\frac{14}{3}.

$$a^{-\frac{14}{3}}\left(b^{\frac{7}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{3} and 2 to get \frac{14}{3}.

$$a^{-\frac{14}{3}}b^{\frac{14}{3}}$$

Expand

$$\left(\frac{b}{a}\right)^{\frac{14}{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and -\frac{4}{3} to get -\frac{7}{3}.

$$\left(a^{-\frac{7}{3}}b^{\frac{1}{3}}b^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add \frac{1}{3} and 2 to get \frac{7}{3}.

$$\left(a^{-\frac{7}{3}}b^{\frac{7}{3}}\right)^{2}$$

Expand \left(a^{-\frac{7}{3}}b^{\frac{7}{3}}\right)^{2}.

$$\left(a^{-\frac{7}{3}}\right)^{2}\left(b^{\frac{7}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{7}{3} and 2 to get -\frac{14}{3}.

$$a^{-\frac{14}{3}}\left(b^{\frac{7}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{3} and 2 to get \frac{14}{3}.

$$a^{-\frac{14}{3}}b^{\frac{14}{3}}$$