Solve -3.2^2+4-{left(3/10right)}^2-16/-2^4

$${ -3.2 }^{ 2 } +4- { \left( \frac{ 3 }{ 10 } \right) }^{ 2 } - \frac{ 16 }{ { -2 }^{ 4 } }$$

Evaluate

$$13.15$$

Solution Steps

Calculate -3.2 to the power of 2 and get 10.24.

$$10.24+4-\left(\frac{3}{10}\right)^{2}-\frac{16}{\left(-2\right)^{4}}$$

Add 10.24 and 4 to get 14.24.

$$14.24-\left(\frac{3}{10}\right)^{2}-\frac{16}{\left(-2\right)^{4}}$$

Calculate \frac{3}{10} to the power of 2 and get \frac{9}{100}.

$$14.24-\frac{9}{100}-\frac{16}{\left(-2\right)^{4}}$$

Convert decimal number 14.24 to fraction \frac{1424}{100}. Reduce the fraction \frac{1424}{100} to lowest terms by extracting and canceling out 4.

$$\frac{356}{25}-\frac{9}{100}-\frac{16}{\left(-2\right)^{4}}$$

Least common multiple of 25 and 100 is 100. Convert \frac{356}{25} and \frac{9}{100} to fractions with denominator 100.

$$\frac{1424}{100}-\frac{9}{100}-\frac{16}{\left(-2\right)^{4}}$$

Since \frac{1424}{100} and \frac{9}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1424-9}{100}-\frac{16}{\left(-2\right)^{4}}$$

Subtract 9 from 1424 to get 1415.

$$\frac{1415}{100}-\frac{16}{\left(-2\right)^{4}}$$

Reduce the fraction \frac{1415}{100} to lowest terms by extracting and canceling out 5.

$$\frac{283}{20}-\frac{16}{\left(-2\right)^{4}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{283}{20}-\frac{16}{16}$$

Divide 16 by 16 to get 1.

$$\frac{283}{20}-1$$

Convert 1 to fraction \frac{20}{20}.

$$\frac{283}{20}-\frac{20}{20}$$

Since \frac{283}{20} and \frac{20}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{283-20}{20}$$

Subtract 20 from 283 to get 263.

$$\frac{263}{20}$$

Factor

$$\frac{263}{5 \cdot 2 ^ {2}} = 13\frac{3}{20} = 13.15$$