Solve 41.6^35.7+101.6^25.7+1.65.7^2+2*1.65.7^3+{5.7}^4-2*1.6*5.7-3{5.7}^3-4*1.6

$$4 { 1.6 }^{ 3 } 5.7+10 { 1.6 }^{ 2 } 5.7+1.6 { 5.7 }^{ 2 } +2 \cdot 1.6 { 5.7 }^{ 3 } + { 5.7 }^{ 4 } -2 \cdot 1.6 \cdot 5.7-3 { 5.7 }^{ 3 } -4 \cdot 1.6$$

Evaluate

$$1359.2915$$

Solution Steps

Calculate 1.6 to the power of 3 and get 4.096.

$$4\times 4.096\times 5.7+10\times 1.6^{2}\times 5.7+1.6\times 5.7^{2}+2\times 1.6\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Multiply 4 and 4.096 to get 16.384.

$$16.384\times 5.7+10\times 1.6^{2}\times 5.7+1.6\times 5.7^{2}+2\times 1.6\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Multiply 16.384 and 5.7 to get 93.3888.

$$93.3888+10\times 1.6^{2}\times 5.7+1.6\times 5.7^{2}+2\times 1.6\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Calculate 1.6 to the power of 2 and get 2.56.

$$93.3888+10\times 2.56\times 5.7+1.6\times 5.7^{2}+2\times 1.6\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Multiply 10 and 2.56 to get 25.6.

$$93.3888+25.6\times 5.7+1.6\times 5.7^{2}+2\times 1.6\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Multiply 25.6 and 5.7 to get 145.92.

$$93.3888+145.92+1.6\times 5.7^{2}+2\times 1.6\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Add 93.3888 and 145.92 to get 239.3088.

$$239.3088+1.6\times 5.7^{2}+2\times 1.6\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Calculate 5.7 to the power of 2 and get 32.49.

$$239.3088+1.6\times 32.49+2\times 1.6\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Multiply 1.6 and 32.49 to get 51.984.

$$239.3088+51.984+2\times 1.6\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Add 239.3088 and 51.984 to get 291.2928.

$$291.2928+2\times 1.6\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Multiply 2 and 1.6 to get 3.2.

$$291.2928+3.2\times 5.7^{3}+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Calculate 5.7 to the power of 3 and get 185.193.

$$291.2928+3.2\times 185.193+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Multiply 3.2 and 185.193 to get 592.6176.

$$291.2928+592.6176+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Add 291.2928 and 592.6176 to get 883.9104.

$$883.9104+5.7^{4}-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Calculate 5.7 to the power of 4 and get 1055.6001.

$$883.9104+1055.6001-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Add 883.9104 and 1055.6001 to get 1939.5105.

$$1939.5105-2\times 1.6\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Multiply 2 and 1.6 to get 3.2.

$$1939.5105-3.2\times 5.7-3\times 5.7^{3}-4\times 1.6$$

Multiply 3.2 and 5.7 to get 18.24.

$$1939.5105-18.24-3\times 5.7^{3}-4\times 1.6$$

Subtract 18.24 from 1939.5105 to get 1921.2705.

$$1921.2705-3\times 5.7^{3}-4\times 1.6$$

Calculate 5.7 to the power of 3 and get 185.193.

$$1921.2705-3\times 185.193-4\times 1.6$$

Multiply 3 and 185.193 to get 555.579.

$$1921.2705-555.579-4\times 1.6$$

Subtract 555.579 from 1921.2705 to get 1365.6915.

$$1365.6915-4\times 1.6$$

Multiply 4 and 1.6 to get 6.4.

$$1365.6915-6.4$$

Subtract 6.4 from 1365.6915 to get 1359.2915.

$$1359.2915$$

Factor

$$\frac{7 \cdot 388369}{2 ^ {4} \cdot 5 ^ {3}} = 1359\frac{583}{2000} = 1359.2915$$