Solve 16left(2^-2right)^4-4left(2^-2right)^-3+2{left({2}^-2right)}^-1-5{left({2}^-2right)}^2

$$16 { \left( { 2 }^{ -2 } \right) }^{ 4 } -4 { \left( { 2 }^{ -2 } \right) }^{ -3 } +2 { \left( { 2 }^{ -2 } \right) }^{ -1 } -5 { \left( { 2 }^{ -2 } \right) }^{ 2 }$$

Evaluate

$$-\frac{993}{4}=-248.25$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and 4 to get -8.

$$16\times 2^{-8}-4\times \left(2^{-2}\right)^{-3}+2\times \left(2^{-2}\right)^{-1}-5\times \left(2^{-2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

$$16\times 2^{-8}-4\times 2^{6}+2\times \left(2^{-2}\right)^{-1}-5\times \left(2^{-2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -1 to get 2.

$$16\times 2^{-8}-4\times 2^{6}+2\times 2^{2}-5\times \left(2^{-2}\right)^{2}$$

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

$$16\times 2^{-8}-4\times 2^{6}+2^{3}-5\times \left(2^{-2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$16\times 2^{-8}-4\times 2^{6}+2^{3}-5\times 2^{-4}$$

Calculate 2 to the power of -8 and get \frac{1}{256}.

$$16\times \frac{1}{256}-4\times 2^{6}+2^{3}-5\times 2^{-4}$$

Multiply 16 and \frac{1}{256} to get \frac{1}{16}.

$$\frac{1}{16}-4\times 2^{6}+2^{3}-5\times 2^{-4}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{1}{16}-4\times 64+2^{3}-5\times 2^{-4}$$

Multiply 4 and 64 to get 256.

$$\frac{1}{16}-256+2^{3}-5\times 2^{-4}$$

Subtract 256 from \frac{1}{16} to get -\frac{4095}{16}.

$$-\frac{4095}{16}+2^{3}-5\times 2^{-4}$$

Calculate 2 to the power of 3 and get 8.

$$-\frac{4095}{16}+8-5\times 2^{-4}$$

Add -\frac{4095}{16} and 8 to get -\frac{3967}{16}.

$$-\frac{3967}{16}-5\times 2^{-4}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$-\frac{3967}{16}-5\times \frac{1}{16}$$

Multiply 5 and \frac{1}{16} to get \frac{5}{16}.

$$-\frac{3967}{16}-\frac{5}{16}$$

Subtract \frac{5}{16} from -\frac{3967}{16} to get -\frac{993}{4}.

$$-\frac{993}{4}$$

Factor

$$-\frac{993}{4} = -248\frac{1}{4} = -248.25$$