Solve (2^{4}*4^{4}):8^{2}-6^{2}+[7-7^3+(2^2*2^3-6*5)]=3^5

$$( 2 ^ { 4 } \times 4 ^ { 4 } ) : 8 ^ { 2 } - 6 ^ { 2 } + [ 7 - 7 ^ { 3 } + ( 2 ^ { 2 } \times 2 ^ { 3 } - 6 \times 5 ) ] = 3 ^ { 5 }$$

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{2^{4}\times 4^{4}}{8^{2}}-6^{2}+7-7^{3}+2^{5}-6\times 5=3^{5}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16\times 4^{4}}{8^{2}}-6^{2}+7-7^{3}+2^{5}-6\times 5=3^{5}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{16\times 256}{8^{2}}-6^{2}+7-7^{3}+2^{5}-6\times 5=3^{5}$$

Multiply 16 and 256 to get 4096.

$$\frac{4096}{8^{2}}-6^{2}+7-7^{3}+2^{5}-6\times 5=3^{5}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{4096}{64}-6^{2}+7-7^{3}+2^{5}-6\times 5=3^{5}$$

Divide 4096 by 64 to get 64.

$$64-6^{2}+7-7^{3}+2^{5}-6\times 5=3^{5}$$

Calculate 6 to the power of 2 and get 36.

$$64-36+7-7^{3}+2^{5}-6\times 5=3^{5}$$

Subtract 36 from 64 to get 28.

$$28+7-7^{3}+2^{5}-6\times 5=3^{5}$$

Calculate 7 to the power of 3 and get 343.

$$28+7-343+2^{5}-6\times 5=3^{5}$$

Subtract 343 from 7 to get -336.

$$28-336+2^{5}-6\times 5=3^{5}$$

Subtract 336 from 28 to get -308.

$$-308+2^{5}-6\times 5=3^{5}$$

Calculate 2 to the power of 5 and get 32.

$$-308+32-6\times 5=3^{5}$$

Multiply 6 and 5 to get 30.

$$-308+32-30=3^{5}$$

Subtract 30 from 32 to get 2.

$$-308+2=3^{5}$$

Add -308 and 2 to get -306.

$$-306=3^{5}$$

Calculate 3 to the power of 5 and get 243.

$$-306=243$$

Compare -306 and 243.

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