Solve 4*7+(-1*5)+3*1/(4^2+-1^2+3^2)*(7^2+{5^2+1)}

$$\frac{ 4 \times 7+(-1 \times 5)+3 \times 1 }{ ( { 4 }^{ 2 } + { -1 }^{ 2 } + { 3 }^{ 2 } ) \times ( { 7 }^{ 2 } + { 5 }^{ 2 } +1) }$$

Evaluate

$$\frac{1}{75}\approx 0.013333333$$

Solution Steps

Multiply 4 and 7 to get 28. Multiply -1 and 5 to get -5. Multiply 3 and 1 to get 3.

$$\frac{28-5+3}{\left(4^{2}+\left(-1\right)^{2}+3^{2}\right)\left(7^{2}+5^{2}+1\right)}$$

Subtract 5 from 28 to get 23.

$$\frac{23+3}{\left(4^{2}+\left(-1\right)^{2}+3^{2}\right)\left(7^{2}+5^{2}+1\right)}$$

Add 23 and 3 to get 26.

$$\frac{26}{\left(4^{2}+\left(-1\right)^{2}+3^{2}\right)\left(7^{2}+5^{2}+1\right)}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{26}{\left(16+\left(-1\right)^{2}+3^{2}\right)\left(7^{2}+5^{2}+1\right)}$$

Calculate -1 to the power of 2 and get 1.

$$\frac{26}{\left(16+1+3^{2}\right)\left(7^{2}+5^{2}+1\right)}$$

Add 16 and 1 to get 17.

$$\frac{26}{\left(17+3^{2}\right)\left(7^{2}+5^{2}+1\right)}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{26}{\left(17+9\right)\left(7^{2}+5^{2}+1\right)}$$

Add 17 and 9 to get 26.

$$\frac{26}{26\left(7^{2}+5^{2}+1\right)}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{26}{26\left(49+5^{2}+1\right)}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{26}{26\left(49+25+1\right)}$$

Add 49 and 25 to get 74.

$$\frac{26}{26\left(74+1\right)}$$

Add 74 and 1 to get 75.

$$\frac{26}{26\times 75}$$

Multiply 26 and 75 to get 1950.

$$\frac{26}{1950}$$

Reduce the fraction \frac{26}{1950} to lowest terms by extracting and canceling out 26.

$$\frac{1}{75}$$

Factor

$$\frac{1}{3 \cdot 5 ^ {2}} = 0.013333333333333334$$