Solve 1^3-(-2^3)-(-2^4)*4^0+{1}^4*2*{2}^-3

$${ 1 }^{ 3 } -(- { 2 }^{ 3 } )-(- { 2 }^{ 4 } ) \times { 4 }^{ 0 } + { 1 }^{ 4 } \times 2 \times { 2 }^{ -3 }$$

Evaluate

$$\frac{101}{4}=25.25$$

Solution Steps

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

$$1^{3}-\left(-2^{3}\right)-\left(-2^{4}\right)\times 4^{0}+1^{4}\times 2^{-2}$$

Calculate 1 to the power of 3 and get 1.

$$1-\left(-2^{3}\right)-\left(-2^{4}\right)\times 4^{0}+1^{4}\times 2^{-2}$$

Calculate 2 to the power of 3 and get 8.

$$1-\left(-8\right)-\left(-2^{4}\right)\times 4^{0}+1^{4}\times 2^{-2}$$

The opposite of -8 is 8.

$$1+8-\left(-2^{4}\right)\times 4^{0}+1^{4}\times 2^{-2}$$

Add 1 and 8 to get 9.

$$9-\left(-2^{4}\right)\times 4^{0}+1^{4}\times 2^{-2}$$

Calculate 2 to the power of 4 and get 16.

$$9-\left(-16\times 4^{0}\right)+1^{4}\times 2^{-2}$$

Calculate 4 to the power of 0 and get 1.

$$9-\left(-16\right)+1^{4}\times 2^{-2}$$

The opposite of -16 is 16.

$$9+16+1^{4}\times 2^{-2}$$

Add 9 and 16 to get 25.

$$25+1^{4}\times 2^{-2}$$

Calculate 1 to the power of 4 and get 1.

$$25+1\times 2^{-2}$$

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

$$25+1\times \frac{1}{4}$$

Multiply 1 and \frac{1}{4} to get \frac{1}{4}.

$$25+\frac{1}{4}$$

Add 25 and \frac{1}{4} to get \frac{101}{4}.

$$\frac{101}{4}$$

Factor

$$\frac{101}{2 ^ {2}} = 25\frac{1}{4} = 25.25$$