Solve (1.6^3+5^-1)-45(1/2)div2^25=?

$$( 1.6 ^ { 3 } + 5 ^ { - 1 } ) - 45 ( \frac { 1 } { 2 } ) \div 2 ^ { 25 } = ?$$

Evaluate

$$4.29599932944774627685546875$$

Solution Steps

Calculate 1.6 to the power of 3 and get 4.096.

$$4.096+5^{-1}-\frac{45\times \frac{1}{2}}{2^{25}}$$

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$4.096+\frac{1}{5}-\frac{45\times \frac{1}{2}}{2^{25}}$$

Add 4.096 and \frac{1}{5} to get \frac{537}{125}.

$$\frac{537}{125}-\frac{45\times \frac{1}{2}}{2^{25}}$$

Multiply 45 and \frac{1}{2} to get \frac{45}{2}.

$$\frac{537}{125}-\frac{\frac{45}{2}}{2^{25}}$$

Calculate 2 to the power of 25 and get 33554432.

$$\frac{537}{125}-\frac{\frac{45}{2}}{33554432}$$

Express \frac{\frac{45}{2}}{33554432} as a single fraction.

$$\frac{537}{125}-\frac{45}{2\times 33554432}$$

Multiply 2 and 33554432 to get 67108864.

$$\frac{537}{125}-\frac{45}{67108864}$$

Subtract \frac{45}{67108864} from \frac{537}{125} to get \frac{36037454343}{8388608000}.

$$\frac{36037454343}{8388608000}$$

Factor

$$\frac{3 \cdot 11 \cdot 23 \cdot 47480177}{2 ^ {26} \cdot 5 ^ {3}} = 4\frac{2483022343}{8388608000} = 4.2959993294477465$$