Solve 1/(0,25)^2+1/(0,5)^3-1/(0,3)^2

$$\frac { 1 } { ( 0,25 ) ^ { 2 } } + \frac { 1 } { ( 0,5 ) ^ { 3 } } - \frac { 1 } { ( 0,3 ) ^ { 2 } }$$

Evaluate

$$\frac{116}{9}\approx 12,888888889$$

Solution Steps

Calculate 0,25 to the power of 2 and get 0,0625.

$$\frac{1}{0,0625}+\frac{1}{0,5^{3}}-\frac{1}{0,3^{2}}$$

Expand \frac{1}{0,0625} by multiplying both numerator and the denominator by 10000.

$$\frac{10000}{625}+\frac{1}{0,5^{3}}-\frac{1}{0,3^{2}}$$

Divide 10000 by 625 to get 16.

$$16+\frac{1}{0,5^{3}}-\frac{1}{0,3^{2}}$$

Calculate 0,5 to the power of 3 and get 0,125.

$$16+\frac{1}{0,125}-\frac{1}{0,3^{2}}$$

Expand \frac{1}{0,125} by multiplying both numerator and the denominator by 1000.

$$16+\frac{1000}{125}-\frac{1}{0,3^{2}}$$

Divide 1000 by 125 to get 8.

$$16+8-\frac{1}{0,3^{2}}$$

Add 16 and 8 to get 24.

$$24-\frac{1}{0,3^{2}}$$

Calculate 0,3 to the power of 2 and get 0,09.

$$24-\frac{1}{0,09}$$

Expand \frac{1}{0,09} by multiplying both numerator and the denominator by 100.

$$24-\frac{100}{9}$$

Convert 24 to fraction \frac{216}{9}.

$$\frac{216}{9}-\frac{100}{9}$$

Since \frac{216}{9} and \frac{100}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{216-100}{9}$$

Subtract 100 from 216 to get 116.

$$\frac{116}{9}$$

Factor

$$\frac{29 \cdot 2 ^ {2}}{3 ^ {2}} = 12\frac{8}{9} = 12.88888888888889$$