Solve 3/-7+[1/5+5]^-2/(frac{3{8}-1/5)^-3div2(frac{1}{4}-5)^-1}

$$\frac { \frac { 3 } { - 7 } + [ \frac { 1 } { 5 } + 5 ] ^ { - 2 } } { ( \frac { 3 } { 8 } - \frac { 1 } { 5 } ) ^ { - 3 } \div 2 ( \frac { 1 } { 4 } - 5 ) ^ { - 1 } }$$

Evaluate

$$\frac{1725143}{86528000}\approx 0.019937396$$

Solution Steps

Fraction \frac{3}{-7} can be rewritten as -\frac{3}{7} by extracting the negative sign.

$$\frac{-\frac{3}{7}+\left(\frac{1}{5}+5\right)^{-2}}{\frac{\left(\frac{3}{8}-\frac{1}{5}\right)^{-3}}{2}\left(\frac{1}{4}-5\right)^{-1}}$$

Add \frac{1}{5} and 5 to get \frac{26}{5}.

$$\frac{-\frac{3}{7}+\left(\frac{26}{5}\right)^{-2}}{\frac{\left(\frac{3}{8}-\frac{1}{5}\right)^{-3}}{2}\left(\frac{1}{4}-5\right)^{-1}}$$

Calculate \frac{26}{5} to the power of -2 and get \frac{25}{676}.

$$\frac{-\frac{3}{7}+\frac{25}{676}}{\frac{\left(\frac{3}{8}-\frac{1}{5}\right)^{-3}}{2}\left(\frac{1}{4}-5\right)^{-1}}$$

Add -\frac{3}{7} and \frac{25}{676} to get -\frac{1853}{4732}.

$$\frac{-\frac{1853}{4732}}{\frac{\left(\frac{3}{8}-\frac{1}{5}\right)^{-3}}{2}\left(\frac{1}{4}-5\right)^{-1}}$$

Subtract \frac{1}{5} from \frac{3}{8} to get \frac{7}{40}.

$$\frac{-\frac{1853}{4732}}{\frac{\left(\frac{7}{40}\right)^{-3}}{2}\left(\frac{1}{4}-5\right)^{-1}}$$

Calculate \frac{7}{40} to the power of -3 and get \frac{64000}{343}.

$$\frac{-\frac{1853}{4732}}{\frac{\frac{64000}{343}}{2}\left(\frac{1}{4}-5\right)^{-1}}$$

Express \frac{\frac{64000}{343}}{2} as a single fraction.

$$\frac{-\frac{1853}{4732}}{\frac{64000}{343\times 2}\left(\frac{1}{4}-5\right)^{-1}}$$

Multiply 343 and 2 to get 686.

$$\frac{-\frac{1853}{4732}}{\frac{64000}{686}\left(\frac{1}{4}-5\right)^{-1}}$$

Reduce the fraction \frac{64000}{686} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{1853}{4732}}{\frac{32000}{343}\left(\frac{1}{4}-5\right)^{-1}}$$

Subtract 5 from \frac{1}{4} to get -\frac{19}{4}.

$$\frac{-\frac{1853}{4732}}{\frac{32000}{343}\left(-\frac{19}{4}\right)^{-1}}$$

Calculate -\frac{19}{4} to the power of -1 and get -\frac{4}{19}.

$$\frac{-\frac{1853}{4732}}{\frac{32000}{343}\left(-\frac{4}{19}\right)}$$

Multiply \frac{32000}{343} and -\frac{4}{19} to get -\frac{128000}{6517}.

$$\frac{-\frac{1853}{4732}}{-\frac{128000}{6517}}$$

Divide -\frac{1853}{4732} by -\frac{128000}{6517} by multiplying -\frac{1853}{4732} by the reciprocal of -\frac{128000}{6517}.

$$-\frac{1853}{4732}\left(-\frac{6517}{128000}\right)$$

Multiply -\frac{1853}{4732} and -\frac{6517}{128000} to get \frac{1725143}{86528000}.

$$\frac{1725143}{86528000}$$

Factor

$$\frac{7 ^ {2} \cdot 17 \cdot 19 \cdot 109}{2 ^ {12} \cdot 5 ^ {3} \cdot 13 ^ {2}} = 0.019937395987426037$$