Solve (-0.125)^12*(-11/3)^7*(-8)^13*(-3/5)^8

$$( - 0.125 ) ^ { 12 } \times ( - 1 \frac { 1 } { 3 } ) ^ { 7 } \times ( - 8 ) ^ { 13 } \times ( - \frac { 3 } { 5 } ) ^ { 8 }$$

Evaluate

$$1.00663296$$

Solution Steps

Calculate -0.125 to the power of 12 and get 0.000000000014551915228366851806640625.

$$0.000000000014551915228366851806640625\left(-\frac{1\times 3+1}{3}\right)^{7}\left(-8\right)^{13}\left(-\frac{3}{5}\right)^{8}$$

Multiply 1 and 3 to get 3.

$$0.000000000014551915228366851806640625\left(-\frac{3+1}{3}\right)^{7}\left(-8\right)^{13}\left(-\frac{3}{5}\right)^{8}$$

Add 3 and 1 to get 4.

$$0.000000000014551915228366851806640625\left(-\frac{4}{3}\right)^{7}\left(-8\right)^{13}\left(-\frac{3}{5}\right)^{8}$$

Calculate -\frac{4}{3} to the power of 7 and get -\frac{16384}{2187}.

$$0.000000000014551915228366851806640625\left(-\frac{16384}{2187}\right)\left(-8\right)^{13}\left(-\frac{3}{5}\right)^{8}$$

Multiply 0.000000000014551915228366851806640625 and -\frac{16384}{2187} to get -\frac{1}{9172942848}.

$$-\frac{1}{9172942848}\left(-8\right)^{13}\left(-\frac{3}{5}\right)^{8}$$

Calculate -8 to the power of 13 and get -549755813888.

$$-\frac{1}{9172942848}\left(-549755813888\right)\left(-\frac{3}{5}\right)^{8}$$

Multiply -\frac{1}{9172942848} and -549755813888 to get \frac{131072}{2187}.

$$\frac{131072}{2187}\left(-\frac{3}{5}\right)^{8}$$

Calculate -\frac{3}{5} to the power of 8 and get \frac{6561}{390625}.

$$\frac{131072}{2187}\times \frac{6561}{390625}$$

Multiply \frac{131072}{2187} and \frac{6561}{390625} to get \frac{393216}{390625}.

$$\frac{393216}{390625}$$

Factor

$$\frac{3 \cdot 2 ^ {17}}{5 ^ {8}} = 1\frac{2591}{390625} = 1.00663296$$