Solve [0.0695^2+1.355+0.2/5][20(5+2)/5^2+25+4]/frac{1{5+1}}

$$\frac { [ \frac { 0.0695 ^ { 2 } + 1.355 + 0.2 } { 5 } ] [ \frac { 20 ( 5 + 2 ) } { 5 ^ { 2 } + 25 + 4 } ] } { \frac { 1 } { 5 + 1 } }$$

Evaluate

$$\frac{43675247}{9000000}\approx 4.852805222$$

Solution Steps

Calculate 0.0695 to the power of 2 and get 0.00483025.

$$\frac{\frac{0.00483025+1.355+0.2}{5}\times \frac{20\left(5+2\right)}{5^{2}+25+4}}{\frac{1}{5+1}}$$

Add 0.00483025 and 1.355 to get 1.35983025.

$$\frac{\frac{1.35983025+0.2}{5}\times \frac{20\left(5+2\right)}{5^{2}+25+4}}{\frac{1}{5+1}}$$

Add 1.35983025 and 0.2 to get 1.55983025.

$$\frac{\frac{1.55983025}{5}\times \frac{20\left(5+2\right)}{5^{2}+25+4}}{\frac{1}{5+1}}$$

Expand \frac{1.55983025}{5} by multiplying both numerator and the denominator by 100000000.

$$\frac{\frac{155983025}{500000000}\times \frac{20\left(5+2\right)}{5^{2}+25+4}}{\frac{1}{5+1}}$$

Reduce the fraction \frac{155983025}{500000000} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{6239321}{20000000}\times \frac{20\left(5+2\right)}{5^{2}+25+4}}{\frac{1}{5+1}}$$

Add 5 and 2 to get 7.

$$\frac{\frac{6239321}{20000000}\times \frac{20\times 7}{5^{2}+25+4}}{\frac{1}{5+1}}$$

Multiply 20 and 7 to get 140.

$$\frac{\frac{6239321}{20000000}\times \frac{140}{5^{2}+25+4}}{\frac{1}{5+1}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\frac{6239321}{20000000}\times \frac{140}{25+25+4}}{\frac{1}{5+1}}$$

Add 25 and 25 to get 50.

$$\frac{\frac{6239321}{20000000}\times \frac{140}{50+4}}{\frac{1}{5+1}}$$

Add 50 and 4 to get 54.

$$\frac{\frac{6239321}{20000000}\times \frac{140}{54}}{\frac{1}{5+1}}$$

Reduce the fraction \frac{140}{54} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{6239321}{20000000}\times \frac{70}{27}}{\frac{1}{5+1}}$$

Multiply \frac{6239321}{20000000} times \frac{70}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{6239321\times 70}{20000000\times 27}}{\frac{1}{5+1}}$$

Do the multiplications in the fraction \frac{6239321\times 70}{20000000\times 27}.

$$\frac{\frac{436752470}{540000000}}{\frac{1}{5+1}}$$

Reduce the fraction \frac{436752470}{540000000} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{43675247}{54000000}}{\frac{1}{5+1}}$$

Add 5 and 1 to get 6.

$$\frac{\frac{43675247}{54000000}}{\frac{1}{6}}$$

Divide \frac{43675247}{54000000} by \frac{1}{6} by multiplying \frac{43675247}{54000000} by the reciprocal of \frac{1}{6}.

$$\frac{43675247}{54000000}\times 6$$

Express \frac{43675247}{54000000}\times 6 as a single fraction.

$$\frac{43675247\times 6}{54000000}$$

Multiply 43675247 and 6 to get 262051482.

$$\frac{262051482}{54000000}$$

Reduce the fraction \frac{262051482}{54000000} to lowest terms by extracting and canceling out 6.

$$\frac{43675247}{9000000}$$

Factor

$$\frac{7 \cdot 11 \cdot 29 \cdot 19559}{2 ^ {6} \cdot 3 ^ {2} \cdot 5 ^ {6}} = 4\frac{7675247}{9000000} = 4.852805222222222$$