Solve [(1/2)^3]^2*(-4/3)^-6:(7/5)^6

$$[ ( \frac { 1 } { 2 } ) ^ { 3 } ] ^ { 2 } \times ( - \frac { 4 } { 3 } ) ^ { - 6 } : ( \frac { 7 } { 5 } ) ^ { 6 }$$

Evaluate

$$\frac{11390625}{30840979456}\approx 0.000369334$$

Solution Steps

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

$$\frac{\left(\frac{1}{2}\right)^{6}\left(-\frac{4}{3}\right)^{-6}}{\left(\frac{7}{5}\right)^{6}}$$

Calculate \frac{1}{2} to the power of 6 and get \frac{1}{64}.

$$\frac{\frac{1}{64}\left(-\frac{4}{3}\right)^{-6}}{\left(\frac{7}{5}\right)^{6}}$$

Calculate -\frac{4}{3} to the power of -6 and get \frac{729}{4096}.

$$\frac{\frac{1}{64}\times \frac{729}{4096}}{\left(\frac{7}{5}\right)^{6}}$$

Multiply \frac{1}{64} and \frac{729}{4096} to get \frac{729}{262144}.

$$\frac{\frac{729}{262144}}{\left(\frac{7}{5}\right)^{6}}$$

Calculate \frac{7}{5} to the power of 6 and get \frac{117649}{15625}.

$$\frac{\frac{729}{262144}}{\frac{117649}{15625}}$$

Divide \frac{729}{262144} by \frac{117649}{15625} by multiplying \frac{729}{262144} by the reciprocal of \frac{117649}{15625}.

$$\frac{729}{262144}\times \frac{15625}{117649}$$

Multiply \frac{729}{262144} and \frac{15625}{117649} to get \frac{11390625}{30840979456}.

$$\frac{11390625}{30840979456}$$

Factor

$$\frac{3 ^ {6} \cdot 5 ^ {6}}{2 ^ {18} \cdot 7 ^ {6}} = 0.0003693340873382669$$