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

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

Evaluate

$$-\frac{762939453124}{9765625}=-78124.999999898$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\left(\frac{1}{5}\right)^{10}-\left(\frac{1}{5}\right)^{-7}$$

Calculate \frac{1}{5} to the power of 10 and get \frac{1}{9765625}.

$$\frac{1}{9765625}-\left(\frac{1}{5}\right)^{-7}$$

Calculate \frac{1}{5} to the power of -7 and get 78125.

$$\frac{1}{9765625}-78125$$

Subtract 78125 from \frac{1}{9765625} to get -\frac{762939453124}{9765625}.

$$-\frac{762939453124}{9765625}$$

Factor

$$-\frac{762939453124}{9765625} = -78124\frac{9765624}{9765625} = -78124.9999998976$$