Solve (2/7)^2*(2/7)^-5/(frac{2{7})^3}

$$\frac { ( \frac { 2 } { 7 } ) ^ { 2 } \times ( \frac { 2 } { 7 } ) ^ { - 5 } } { ( \frac { 2 } { 7 } ) ^ { 3 } }$$

Evaluate

$$\frac{117649}{64}=1838.265625$$

Solution Steps

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

$$\frac{\left(\frac{2}{7}\right)^{-3}}{\left(\frac{2}{7}\right)^{3}}$$

Rewrite \left(\frac{2}{7}\right)^{3} as \left(\frac{2}{7}\right)^{-3}\times \left(\frac{2}{7}\right)^{6}. Cancel out \left(\frac{2}{7}\right)^{-3} in both numerator and denominator.

$$\frac{1}{\left(\frac{2}{7}\right)^{6}}$$

Calculate \frac{2}{7} to the power of 6 and get \frac{64}{117649}.

$$\frac{1}{\frac{64}{117649}}$$

Divide 1 by \frac{64}{117649} by multiplying 1 by the reciprocal of \frac{64}{117649}.

$$1\times \frac{117649}{64}$$

Multiply 1 and \frac{117649}{64} to get \frac{117649}{64}.

$$\frac{117649}{64}$$

Factor

$$\frac{7 ^ {6}}{2 ^ {6}} = 1838\frac{17}{64} = 1838.265625$$