Solve 2^4-(1-0.5)*1/3*[2-(-3)^2]=

$$2 ^ { 4 } - ( 1 - 0.5 ) \times \frac { 1 } { 3 } \times [ 2 - ( - 3 ) ^ { 2 } ] =$$

Evaluate

$$\frac{103}{6}\approx 17.166666667$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$16-\left(1-0.5\right)\times \frac{1}{3}\left(2-\left(-3\right)^{2}\right)$$

Subtract 0.5 from 1 to get 0.5.

$$16-0.5\times \frac{1}{3}\left(2-\left(-3\right)^{2}\right)$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$16-\frac{1}{2}\times \frac{1}{3}\left(2-\left(-3\right)^{2}\right)$$

Multiply \frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$16-\frac{1\times 1}{2\times 3}\left(2-\left(-3\right)^{2}\right)$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 3}.

$$16-\frac{1}{6}\left(2-\left(-3\right)^{2}\right)$$

Calculate -3 to the power of 2 and get 9.

$$16-\frac{1}{6}\left(2-9\right)$$

Subtract 9 from 2 to get -7.

$$16-\frac{1}{6}\left(-7\right)$$

Multiply \frac{1}{6} and -7 to get \frac{-7}{6}.

$$16-\frac{-7}{6}$$

Fraction \frac{-7}{6} can be rewritten as -\frac{7}{6} by extracting the negative sign.

$$16-\left(-\frac{7}{6}\right)$$

The opposite of -\frac{7}{6} is \frac{7}{6}.

$$16+\frac{7}{6}$$

Convert 16 to fraction \frac{96}{6}.

$$\frac{96}{6}+\frac{7}{6}$$

Since \frac{96}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{96+7}{6}$$

Add 96 and 7 to get 103.

$$\frac{103}{6}$$

Factor

$$\frac{103}{2 \cdot 3} = 17\frac{1}{6} = 17.166666666666668$$