Solve -0.5^2+1/4-|-3^2-9|-(-11/2)^3*16/27

$$- 0.5 ^ { 2 } + \frac { 1 } { 4 } - | - 3 ^ { 2 } - 9 | - ( - 1 \frac { 1 } { 2 } ) ^ { 3 } \times \frac { 16 } { 27 }$$

Evaluate

$$-16$$

Solution Steps

Calculate 0.5 to the power of 2 and get 0.25.

$$-0.25+\frac{1}{4}-|-3^{2}-9|-\left(-\frac{1\times 2+1}{2}\right)^{3}\times \frac{16}{27}$$

Add -0.25 and \frac{1}{4} to get 0.

$$0-|-3^{2}-9|-\left(-\frac{1\times 2+1}{2}\right)^{3}\times \frac{16}{27}$$

Calculate 3 to the power of 2 and get 9.

$$0-|-9-9|-\left(-\frac{1\times 2+1}{2}\right)^{3}\times \frac{16}{27}$$

Subtract 9 from -9 to get -18.

$$0-|-18|-\left(-\frac{1\times 2+1}{2}\right)^{3}\times \frac{16}{27}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -18 is 18.

$$0-18-\left(-\frac{1\times 2+1}{2}\right)^{3}\times \frac{16}{27}$$

Subtract 18 from 0 to get -18.

$$-18-\left(-\frac{1\times 2+1}{2}\right)^{3}\times \frac{16}{27}$$

Multiply 1 and 2 to get 2.

$$-18-\left(-\frac{2+1}{2}\right)^{3}\times \frac{16}{27}$$

Add 2 and 1 to get 3.

$$-18-\left(-\frac{3}{2}\right)^{3}\times \frac{16}{27}$$

Calculate -\frac{3}{2} to the power of 3 and get -\frac{27}{8}.

$$-18-\left(-\frac{27}{8}\times \frac{16}{27}\right)$$

Multiply -\frac{27}{8} and \frac{16}{27} to get -2.

$$-18-\left(-2\right)$$

The opposite of -2 is 2.

$$-18+2$$

Add -18 and 2 to get -16.

$$-16$$

Factor

$$-16$$