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

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

Evaluate

$$-\frac{12799657}{4096}\approx -3124.916259766$$

Solution Steps

Divide 6 by 2 to get 3.

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

Add \frac{1}{5} and 3 to get \frac{16}{5}.

$$\left(\frac{\frac{16}{5}}{\frac{7}{5}}\right)^{-3}-\left(\frac{1}{5}\right)^{-5}$$

Divide \frac{16}{5} by \frac{7}{5} by multiplying \frac{16}{5} by the reciprocal of \frac{7}{5}.

$$\left(\frac{16}{5}\times \frac{5}{7}\right)^{-3}-\left(\frac{1}{5}\right)^{-5}$$

Multiply \frac{16}{5} and \frac{5}{7} to get \frac{16}{7}.

$$\left(\frac{16}{7}\right)^{-3}-\left(\frac{1}{5}\right)^{-5}$$

Calculate \frac{16}{7} to the power of -3 and get \frac{343}{4096}.

$$\frac{343}{4096}-\left(\frac{1}{5}\right)^{-5}$$

Calculate \frac{1}{5} to the power of -5 and get 3125.

$$\frac{343}{4096}-3125$$

Subtract 3125 from \frac{343}{4096} to get -\frac{12799657}{4096}.

$$-\frac{12799657}{4096}$$

Factor

$$-\frac{12799657}{4096} = -3124\frac{3753}{4096} = -3124.916259765625$$