Solve 237.765*0.749^2-10.531*0.749^2*0.749^2-52.775*0.749^2*0.749

$$237.765 \times { 0.749 }^{ 2 } -10.531 \times { 0.749 }^{ 2 } \times { 0.749 }^{ 2 } -52.775 \times { 0.749 }^{ 2 } \times 0.749$$

Evaluate

$$107.896550094732469$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$237.765\times 0.749^{2}-10.531\times 0.749^{4}-52.775\times 0.749^{2}\times 0.749$$

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

$$237.765\times 0.749^{2}-10.531\times 0.749^{4}-52.775\times 0.749^{3}$$

Calculate 0.749 to the power of 2 and get 0.561001.

$$237.765\times 0.561001-10.531\times 0.749^{4}-52.775\times 0.749^{3}$$

Multiply 237.765 and 0.561001 to get 133.386402765.

$$133.386402765-10.531\times 0.749^{4}-52.775\times 0.749^{3}$$

Calculate 0.749 to the power of 4 and get 0.314722122001.

$$133.386402765-10.531\times 0.314722122001-52.775\times 0.749^{3}$$

Multiply 10.531 and 0.314722122001 to get 3.314338666792531.

$$133.386402765-3.314338666792531-52.775\times 0.749^{3}$$

Subtract 3.314338666792531 from 133.386402765 to get 130.072064098207469.

$$130.072064098207469-52.775\times 0.749^{3}$$

Calculate 0.749 to the power of 3 and get 0.420189749.

$$130.072064098207469-52.775\times 0.420189749$$

Multiply 52.775 and 0.420189749 to get 22.175514003475.

$$130.072064098207469-22.175514003475$$

Subtract 22.175514003475 from 130.072064098207469 to get 107.896550094732469.

$$107.896550094732469$$

Factor

$$\frac{349 \cdot 1289 \cdot 427529 \cdot 7 ^ {2} \cdot 107 ^ {2}}{2 ^ {15} \cdot 5 ^ {15}} = 107\frac{896550094732464}{1000000000000000} = 107.89655009473246$$