Solve [(-5/7)^2]^4*[(-7/5)^3]^3

$$[ ( - \frac { 5 } { 7 } ) ^ { 2 } ] ^ { 4 } \times [ ( - \frac { 7 } { 5 } ) ^ { 3 } ] ^ { 3 }$$

Evaluate

$$-\frac{7}{5}=-1.4$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\left(-\frac{5}{7}\right)^{8}\left(\left(-\frac{7}{5}\right)^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-\frac{5}{7}\right)^{8}\left(-\frac{7}{5}\right)^{9}$$

Calculate -\frac{5}{7} to the power of 8 and get \frac{390625}{5764801}.

$$\frac{390625}{5764801}\left(-\frac{7}{5}\right)^{9}$$

Calculate -\frac{7}{5} to the power of 9 and get -\frac{40353607}{1953125}.

$$\frac{390625}{5764801}\left(-\frac{40353607}{1953125}\right)$$

Multiply \frac{390625}{5764801} and -\frac{40353607}{1953125} to get -\frac{7}{5}.

$$-\frac{7}{5}$$

Factor

$$-\frac{7}{5} = -1\frac{2}{5} = -1.4$$