Solve 8^{6}-7^{6}:7/8^{3+7^{3}}*8/8^8-7^8:7/8^4+7^4

$$8 ^ { 6 } - 7 ^ { 6 } : \frac { 7 } { 8 ^ { 3 } + 7 ^ { 3 } } \cdot \frac { 8 } { 8 ^ { 8 } - 7 ^ { 8 } } : \frac { 7 } { 8 ^ { 4 } + 7 ^ { 4 } }$$

Evaluate

$$\frac{28527416}{113}\approx 252455.008849558$$

Solution Steps

Calculate 8 to the power of 6 and get 262144.

$$262144-\frac{\frac{7^{6}}{\frac{7}{8^{3}+7^{3}}}\times \frac{8}{8^{8}-7^{8}}}{\frac{7}{8^{4}+7^{4}}}$$

Calculate 7 to the power of 6 and get 117649.

$$262144-\frac{\frac{117649}{\frac{7}{8^{3}+7^{3}}}\times \frac{8}{8^{8}-7^{8}}}{\frac{7}{8^{4}+7^{4}}}$$

Calculate 8 to the power of 3 and get 512.

$$262144-\frac{\frac{117649}{\frac{7}{512+7^{3}}}\times \frac{8}{8^{8}-7^{8}}}{\frac{7}{8^{4}+7^{4}}}$$

Calculate 7 to the power of 3 and get 343.

$$262144-\frac{\frac{117649}{\frac{7}{512+343}}\times \frac{8}{8^{8}-7^{8}}}{\frac{7}{8^{4}+7^{4}}}$$

Add 512 and 343 to get 855.

$$262144-\frac{\frac{117649}{\frac{7}{855}}\times \frac{8}{8^{8}-7^{8}}}{\frac{7}{8^{4}+7^{4}}}$$

Divide 117649 by \frac{7}{855} by multiplying 117649 by the reciprocal of \frac{7}{855}.

$$262144-\frac{117649\times \frac{855}{7}\times \frac{8}{8^{8}-7^{8}}}{\frac{7}{8^{4}+7^{4}}}$$

Express 117649\times \frac{855}{7} as a single fraction.

$$262144-\frac{\frac{117649\times 855}{7}\times \frac{8}{8^{8}-7^{8}}}{\frac{7}{8^{4}+7^{4}}}$$

Multiply 117649 and 855 to get 100589895.

$$262144-\frac{\frac{100589895}{7}\times \frac{8}{8^{8}-7^{8}}}{\frac{7}{8^{4}+7^{4}}}$$

Divide 100589895 by 7 to get 14369985.

$$262144-\frac{14369985\times \frac{8}{8^{8}-7^{8}}}{\frac{7}{8^{4}+7^{4}}}$$

Calculate 8 to the power of 8 and get 16777216.

$$262144-\frac{14369985\times \frac{8}{16777216-7^{8}}}{\frac{7}{8^{4}+7^{4}}}$$

Calculate 7 to the power of 8 and get 5764801.

$$262144-\frac{14369985\times \frac{8}{16777216-5764801}}{\frac{7}{8^{4}+7^{4}}}$$

Subtract 5764801 from 16777216 to get 11012415.

$$262144-\frac{14369985\times \frac{8}{11012415}}{\frac{7}{8^{4}+7^{4}}}$$

Express 14369985\times \frac{8}{11012415} as a single fraction.

$$262144-\frac{\frac{14369985\times 8}{11012415}}{\frac{7}{8^{4}+7^{4}}}$$

Multiply 14369985 and 8 to get 114959880.

$$262144-\frac{\frac{114959880}{11012415}}{\frac{7}{8^{4}+7^{4}}}$$

Reduce the fraction \frac{114959880}{11012415} to lowest terms by extracting and canceling out 15.

$$262144-\frac{\frac{7663992}{734161}}{\frac{7}{8^{4}+7^{4}}}$$

Calculate 8 to the power of 4 and get 4096.

$$262144-\frac{\frac{7663992}{734161}}{\frac{7}{4096+7^{4}}}$$

Calculate 7 to the power of 4 and get 2401.

$$262144-\frac{\frac{7663992}{734161}}{\frac{7}{4096+2401}}$$

Add 4096 and 2401 to get 6497.

$$262144-\frac{\frac{7663992}{734161}}{\frac{7}{6497}}$$

Divide \frac{7663992}{734161} by \frac{7}{6497} by multiplying \frac{7663992}{734161} by the reciprocal of \frac{7}{6497}.

$$262144-\frac{7663992}{734161}\times \frac{6497}{7}$$

Multiply \frac{7663992}{734161} times \frac{6497}{7} by multiplying numerator times numerator and denominator times denominator.

$$262144-\frac{7663992\times 6497}{734161\times 7}$$

Do the multiplications in the fraction \frac{7663992\times 6497}{734161\times 7}.

$$262144-\frac{49792956024}{5139127}$$

Reduce the fraction \frac{49792956024}{5139127} to lowest terms by extracting and canceling out 45479.

$$262144-\frac{1094856}{113}$$

Convert 262144 to fraction \frac{29622272}{113}.

$$\frac{29622272}{113}-\frac{1094856}{113}$$

Since \frac{29622272}{113} and \frac{1094856}{113} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29622272-1094856}{113}$$

Subtract 1094856 from 29622272 to get 28527416.

$$\frac{28527416}{113}$$

Factor

$$\frac{2 ^ {3} \cdot 29 \cdot 122963}{113} = 252455\frac{1}{113} = 252455.00884955752$$