Solve (14.2^{3}-6.2^3+8.2^3)^2=2^14

$$( 14.2 ^ { 3 } - 6.2 ^ { 3 } + 8.2 ^ { 3 } ) ^ { 2 } = 2 ^ { 14 }$$

Verify

Solution Steps

Calculate 14.2 to the power of 3 and get 2863.288.

$$\left(2863.288-6.2^{3}+8.2^{3}\right)^{2}=2^{14}$$

Calculate 6.2 to the power of 3 and get 238.328.

$$\left(2863.288-238.328+8.2^{3}\right)^{2}=2^{14}$$

Subtract 238.328 from 2863.288 to get 2624.96.

$$\left(2624.96+8.2^{3}\right)^{2}=2^{14}$$

Calculate 8.2 to the power of 3 and get 551.368.

$$\left(2624.96+551.368\right)^{2}=2^{14}$$

Add 2624.96 and 551.368 to get 3176.328.

$$3176.328^{2}=2^{14}$$

Calculate 3176.328 to the power of 2 and get 10089059.563584.

$$10089059.563584=2^{14}$$

Calculate 2 to the power of 14 and get 16384.

$$10089059.563584=16384$$

Compare 10089059.563584 and 16384.

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