Solve (-3/5)^-3-3quadtext{18.}8^-10/8^-8

$$( - \frac { 3 } { 5 } ) ^ { - 3 } - 3 \quad \text { 18. } \frac { 8 ^ { - 10 } } { 8 ^ { - 8 } }$$

Evaluate

$$-\frac{4729}{864}\approx -5.47337963$$

Solution Steps

Rewrite 8^{-8} as 8^{-10}\times 8^{2}. Cancel out 8^{-10} in both numerator and denominator.

$$\left(-\frac{3}{5}\right)^{-3}-3\times 18\times \frac{1}{8^{2}}$$

Calculate -\frac{3}{5} to the power of -3 and get -\frac{125}{27}.

$$-\frac{125}{27}-3\times 18\times \frac{1}{8^{2}}$$

Multiply 3 and 18 to get 54.

$$-\frac{125}{27}-54\times \frac{1}{8^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$-\frac{125}{27}-54\times \frac{1}{64}$$

Multiply 54 and \frac{1}{64} to get \frac{27}{32}.

$$-\frac{125}{27}-\frac{27}{32}$$

Subtract \frac{27}{32} from -\frac{125}{27} to get -\frac{4729}{864}.

$$-\frac{4729}{864}$$

Factor

$$-\frac{4729}{864} = -5\frac{409}{864} = -5.47337962962963$$