Solve 5left(1/5^2-1/2^4right)/5^2

$$\frac{ 5 \left( \frac{ 1 }{ { 5 }^{ 2 } } - \frac{ 1 }{ { 2 }^{ 4 } } \right) }{ { 5 }^{ 2 } }$$

Evaluate

$$-\frac{9}{2000}=-0.0045$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{5\left(\frac{1}{25}-\frac{1}{2^{4}}\right)}{5^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{5\left(\frac{1}{25}-\frac{1}{16}\right)}{5^{2}}$$

Least common multiple of 25 and 16 is 400. Convert \frac{1}{25} and \frac{1}{16} to fractions with denominator 400.

$$\frac{5\left(\frac{16}{400}-\frac{25}{400}\right)}{5^{2}}$$

Since \frac{16}{400} and \frac{25}{400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times \frac{16-25}{400}}{5^{2}}$$

Subtract 25 from 16 to get -9.

$$\frac{5\left(-\frac{9}{400}\right)}{5^{2}}$$

Express 5\left(-\frac{9}{400}\right) as a single fraction.

$$\frac{\frac{5\left(-9\right)}{400}}{5^{2}}$$

Multiply 5 and -9 to get -45.

$$\frac{\frac{-45}{400}}{5^{2}}$$

Reduce the fraction \frac{-45}{400} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{9}{80}}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{-\frac{9}{80}}{25}$$

Express \frac{-\frac{9}{80}}{25} as a single fraction.

$$\frac{-9}{80\times 25}$$

Multiply 80 and 25 to get 2000.

$$\frac{-9}{2000}$$

Fraction \frac{-9}{2000} can be rewritten as -\frac{9}{2000} by extracting the negative sign.

$$-\frac{9}{2000}$$

Factor

$$-\frac{9}{2000} = -0.0045$$