Solve 5^4/8-5^3/4+5^2/2=-5^2/8

$$\frac { 5 ^ { 4 } } { 8 } - \frac { 5 ^ { 3 } } { 4 } + \frac { 5 ^ { 2 } } { 2 } = - \frac { 5 ^ { 2 } } { 8 }$$

Verify

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 8,4,2.

$$5^{4}-2\times 5^{3}+4\times 5^{2}=-5^{2}$$

Calculate 5 to the power of 4 and get 625.

$$625-2\times 5^{3}+4\times 5^{2}=-5^{2}$$

Calculate 5 to the power of 3 and get 125.

$$625-2\times 125+4\times 5^{2}=-5^{2}$$

Multiply -2 and 125 to get -250.

$$625-250+4\times 5^{2}=-5^{2}$$

Subtract 250 from 625 to get 375.

$$375+4\times 5^{2}=-5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$375+4\times 25=-5^{2}$$

Multiply 4 and 25 to get 100.

$$375+100=-5^{2}$$

Add 375 and 100 to get 475.

$$475=-5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$475=-25$$

Compare 475 and -25.

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