Solve [(-2/5)^2div(-2/5)^5]^2

$$[ ( \frac { - 2 } { 5 } ) ^ { 2 } \div ( \frac { - 2 } { 5 } ) ^ { 5 } ] ^ { 2 }$$

Evaluate

$$\frac{15625}{64}=244.140625$$

Solution Steps

Rewrite \left(\frac{-2}{5}\right)^{5} as \left(\frac{-2}{5}\right)^{2}\times \left(\frac{-2}{5}\right)^{3}. Cancel out \left(\frac{-2}{5}\right)^{2} in both numerator and denominator.

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

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

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

Calculate -\frac{2}{5} to the power of 3 and get -\frac{8}{125}.

$$\left(\frac{1}{-\frac{8}{125}}\right)^{2}$$

Divide 1 by -\frac{8}{125} by multiplying 1 by the reciprocal of -\frac{8}{125}.

$$\left(1\left(-\frac{125}{8}\right)\right)^{2}$$

Multiply 1 and -\frac{125}{8} to get -\frac{125}{8}.

$$\left(-\frac{125}{8}\right)^{2}$$

Calculate -\frac{125}{8} to the power of 2 and get \frac{15625}{64}.

$$\frac{15625}{64}$$

Factor

$$\frac{5 ^ {6}}{2 ^ {6}} = 244\frac{9}{64} = 244.140625$$