Solve (2)(-2)^{3}*2^2*(-2)^4+2^5*(-2)^4

$$( 2 ) ( - 2 ) ^ { 3 } \times 2 ^ { 2 } \times ( - 2 ) ^ { 4 } + 2 ^ { 5 } \times ( - 2 ) ^ { 4 }$$

Evaluate

$$-512$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2^{3}\left(-2\right)^{3}\left(-2\right)^{4}+2^{5}\left(-2\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$2^{3}\left(-2\right)^{7}+2^{5}\left(-2\right)^{4}$$

Calculate 2 to the power of 3 and get 8.

$$8\left(-2\right)^{7}+2^{5}\left(-2\right)^{4}$$

Calculate -2 to the power of 7 and get -128.

$$8\left(-128\right)+2^{5}\left(-2\right)^{4}$$

Multiply 8 and -128 to get -1024.

$$-1024+2^{5}\left(-2\right)^{4}$$

Calculate 2 to the power of 5 and get 32.

$$-1024+32\left(-2\right)^{4}$$

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

$$-1024+32\times 16$$

Multiply 32 and 16 to get 512.

$$-1024+512$$

Add -1024 and 512 to get -512.

$$-512$$

Factor

$$-512$$