Solve |(-2)^{2}*2^3-3^3|+3^3+2009-(-1)^101

$$| ( - 2 ) ^ { 2 } \cdot 2 ^ { 3 } - 3 ^ { 3 } | + 3 ^ { 3 } + 2009 - ( - 1 ) ^ { 101 }$$

Evaluate

$$2042$$

Solution Steps

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

$$|4\times 2^{3}-3^{3}|+3^{3}+2009-\left(-1\right)^{101}$$

Calculate 2 to the power of 3 and get 8.

$$|4\times 8-3^{3}|+3^{3}+2009-\left(-1\right)^{101}$$

Multiply 4 and 8 to get 32.

$$|32-3^{3}|+3^{3}+2009-\left(-1\right)^{101}$$

Calculate 3 to the power of 3 and get 27.

$$|32-27|+3^{3}+2009-\left(-1\right)^{101}$$

Subtract 27 from 32 to get 5.

$$|5|+3^{3}+2009-\left(-1\right)^{101}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 5 is 5.

$$5+3^{3}+2009-\left(-1\right)^{101}$$

Calculate 3 to the power of 3 and get 27.

$$5+27+2009-\left(-1\right)^{101}$$

Add 5 and 27 to get 32.

$$32+2009-\left(-1\right)^{101}$$

Add 32 and 2009 to get 2041.

$$2041-\left(-1\right)^{101}$$

Calculate -1 to the power of 101 and get -1.

$$2041-\left(-1\right)$$

The opposite of -1 is 1.

$$2041+1$$

Add 2041 and 1 to get 2042.

$$2042$$

Factor

$$2\times 1021$$