Solve {l}{(1.3)^{2}*0.3^2+(0.3)^2*0.3}{+(2-1.3)^2*0.2+(1.7)^2*0.2}

$$\left. \begin{array} { l } { ( 1.3 ) ^ { 2 } \times 0.3 ^ { 2 } + ( 0.3 ) ^ { 2 } \times 0.3 } \\ { + ( 2 - 1.3 ) ^ { 2 } \times 0.2 + ( 1.7 ) ^ { 2 } \times 0.2 } \end{array} \right.$$

Evaluate

$$0.8551$$

Solution Steps

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

$$1.3^{2}\times 0.3^{2}+0.3^{3}+\left(2-1.3\right)^{2}\times 0.2+1.7^{2}\times 0.2$$

Calculate 1.3 to the power of 2 and get 1.69.

$$1.69\times 0.3^{2}+0.3^{3}+\left(2-1.3\right)^{2}\times 0.2+1.7^{2}\times 0.2$$

Calculate 0.3 to the power of 2 and get 0.09.

$$1.69\times 0.09+0.3^{3}+\left(2-1.3\right)^{2}\times 0.2+1.7^{2}\times 0.2$$

Multiply 1.69 and 0.09 to get 0.1521.

$$0.1521+0.3^{3}+\left(2-1.3\right)^{2}\times 0.2+1.7^{2}\times 0.2$$

Calculate 0.3 to the power of 3 and get 0.027.

$$0.1521+0.027+\left(2-1.3\right)^{2}\times 0.2+1.7^{2}\times 0.2$$

Add 0.1521 and 0.027 to get 0.1791.

$$0.1791+\left(2-1.3\right)^{2}\times 0.2+1.7^{2}\times 0.2$$

Subtract 1.3 from 2 to get 0.7.

$$0.1791+0.7^{2}\times 0.2+1.7^{2}\times 0.2$$

Calculate 0.7 to the power of 2 and get 0.49.

$$0.1791+0.49\times 0.2+1.7^{2}\times 0.2$$

Multiply 0.49 and 0.2 to get 0.098.

$$0.1791+0.098+1.7^{2}\times 0.2$$

Add 0.1791 and 0.098 to get 0.2771.

$$0.2771+1.7^{2}\times 0.2$$

Calculate 1.7 to the power of 2 and get 2.89.

$$0.2771+2.89\times 0.2$$

Multiply 2.89 and 0.2 to get 0.578.

$$0.2771+0.578$$

Add 0.2771 and 0.578 to get 0.8551.

$$0.8551$$

Factor

$$\frac{17 \cdot 503}{2 ^ {4} \cdot 5 ^ {4}} = 0.8551$$