Solve 1/15*((1*4)^2*1+(3*4)^2-4+(4*4)^2*3+(5*4)^2*7)

$$\frac { 1 } { 15 } \cdot ( ( 1 \cdot 4 ) ^ { 2 } \cdot 1 + ( 3 \cdot 4 ) ^ { 2 } - 4 + ( 4 \cdot 4 ) ^ { 2 } \cdot 3 + ( 5 \cdot 4 ) ^ { 2 } \cdot 7 )$$

Evaluate

$$\frac{3724}{15}\approx 248.266666667$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{1}{15}\left(4^{2}\times 1+\left(3\times 4\right)^{2}-4+\left(4\times 4\right)^{2}\times 3+\left(5\times 4\right)^{2}\times 7\right)$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{15}\left(16\times 1+\left(3\times 4\right)^{2}-4+\left(4\times 4\right)^{2}\times 3+\left(5\times 4\right)^{2}\times 7\right)$$

Multiply 16 and 1 to get 16.

$$\frac{1}{15}\left(16+\left(3\times 4\right)^{2}-4+\left(4\times 4\right)^{2}\times 3+\left(5\times 4\right)^{2}\times 7\right)$$

Multiply 3 and 4 to get 12.

$$\frac{1}{15}\left(16+12^{2}-4+\left(4\times 4\right)^{2}\times 3+\left(5\times 4\right)^{2}\times 7\right)$$

Calculate 12 to the power of 2 and get 144.

$$\frac{1}{15}\left(16+144-4+\left(4\times 4\right)^{2}\times 3+\left(5\times 4\right)^{2}\times 7\right)$$

Add 16 and 144 to get 160.

$$\frac{1}{15}\left(160-4+\left(4\times 4\right)^{2}\times 3+\left(5\times 4\right)^{2}\times 7\right)$$

Subtract 4 from 160 to get 156.

$$\frac{1}{15}\left(156+\left(4\times 4\right)^{2}\times 3+\left(5\times 4\right)^{2}\times 7\right)$$

Multiply 4 and 4 to get 16.

$$\frac{1}{15}\left(156+16^{2}\times 3+\left(5\times 4\right)^{2}\times 7\right)$$

Calculate 16 to the power of 2 and get 256.

$$\frac{1}{15}\left(156+256\times 3+\left(5\times 4\right)^{2}\times 7\right)$$

Multiply 256 and 3 to get 768.

$$\frac{1}{15}\left(156+768+\left(5\times 4\right)^{2}\times 7\right)$$

Add 156 and 768 to get 924.

$$\frac{1}{15}\left(924+\left(5\times 4\right)^{2}\times 7\right)$$

Multiply 5 and 4 to get 20.

$$\frac{1}{15}\left(924+20^{2}\times 7\right)$$

Calculate 20 to the power of 2 and get 400.

$$\frac{1}{15}\left(924+400\times 7\right)$$

Multiply 400 and 7 to get 2800.

$$\frac{1}{15}\left(924+2800\right)$$

Add 924 and 2800 to get 3724.

$$\frac{1}{15}\times 3724$$

Multiply \frac{1}{15} and 3724 to get \frac{3724}{15}.

$$\frac{3724}{15}$$

Factor

$$\frac{2 ^ {2} \cdot 7 ^ {2} \cdot 19}{3 \cdot 5} = 248\frac{4}{15} = 248.26666666666668$$