Solve 7^3-[4+5(4.25div17/34)]+(1/4)^2

$$7 ^ { 3 } - [ 4 + 5 ( 4.25 \div \frac { 17 } { 34 } ) ] + ( \frac { 1 } { 4 } ) ^ { 2 }$$

Evaluate

$$296.5625$$

Solution Steps

Calculate 7 to the power of 3 and get 343.

$$343-\left(4+5\times \frac{4.25}{\frac{17}{34}}\right)+\left(\frac{1}{4}\right)^{2}$$

Divide 4.25 by \frac{17}{34} by multiplying 4.25 by the reciprocal of \frac{17}{34}.

$$343-\left(4+5\times \frac{4.25\times 34}{17}\right)+\left(\frac{1}{4}\right)^{2}$$

Multiply 4.25 and 34 to get 144.5.

$$343-\left(4+5\times \frac{144.5}{17}\right)+\left(\frac{1}{4}\right)^{2}$$

Expand \frac{144.5}{17} by multiplying both numerator and the denominator by 10.

$$343-\left(4+5\times \frac{1445}{170}\right)+\left(\frac{1}{4}\right)^{2}$$

Reduce the fraction \frac{1445}{170} to lowest terms by extracting and canceling out 85.

$$343-\left(4+5\times \frac{17}{2}\right)+\left(\frac{1}{4}\right)^{2}$$

Express 5\times \frac{17}{2} as a single fraction.

$$343-\left(4+\frac{5\times 17}{2}\right)+\left(\frac{1}{4}\right)^{2}$$

Multiply 5 and 17 to get 85.

$$343-\left(4+\frac{85}{2}\right)+\left(\frac{1}{4}\right)^{2}$$

Convert 4 to fraction \frac{8}{2}.

$$343-\left(\frac{8}{2}+\frac{85}{2}\right)+\left(\frac{1}{4}\right)^{2}$$

Since \frac{8}{2} and \frac{85}{2} have the same denominator, add them by adding their numerators.

$$343-\frac{8+85}{2}+\left(\frac{1}{4}\right)^{2}$$

Add 8 and 85 to get 93.

$$343-\frac{93}{2}+\left(\frac{1}{4}\right)^{2}$$

Convert 343 to fraction \frac{686}{2}.

$$\frac{686}{2}-\frac{93}{2}+\left(\frac{1}{4}\right)^{2}$$

Since \frac{686}{2} and \frac{93}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{686-93}{2}+\left(\frac{1}{4}\right)^{2}$$

Subtract 93 from 686 to get 593.

$$\frac{593}{2}+\left(\frac{1}{4}\right)^{2}$$

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

$$\frac{593}{2}+\frac{1}{16}$$

Least common multiple of 2 and 16 is 16. Convert \frac{593}{2} and \frac{1}{16} to fractions with denominator 16.

$$\frac{4744}{16}+\frac{1}{16}$$

Since \frac{4744}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{4744+1}{16}$$

Add 4744 and 1 to get 4745.

$$\frac{4745}{16}$$

Factor

$$\frac{5 \cdot 13 \cdot 73}{2 ^ {4}} = 296\frac{9}{16} = 296.5625$$