What is expand-14/27+(7(2^{39}+3^{39}))/(2^{38)*45} ?

The solution to expand-14/27+(7(2^{39}+3^{39}))/(2^{38)*45} is -14/27+14/45+(3^{37}*7)/(2^{38)*5}

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expand-14/27+(7(2^{39}+3^{39}))/(2^{38)*45}

expand

- \frac{14}{27} + \frac{7 ( 2 ^{39} + 3 ^{39} )}{2 ^{38} \cdot 45}

- \frac{14}{27} + \frac{14}{45} + \frac{3 ^{37} \cdot 7}{2 ^{38} \cdot 5}

Decimal Notation

2293372.42212 \dots

Solution steps

- \frac{14}{27} + \frac{7 ( 2 ^{39} + 3 ^{39} )}{2 ^{38} \cdot 45}

Expand

7 (2^{39} + 3^{39}) : 2^{39} \cdot 7 + 3^{39} \cdot 7

= - \frac{14}{27} + \frac{2 ^{39} \cdot 7 + 3 ^{39} \cdot 7}{2 ^{38} \cdot 45}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 ^{39} \cdot 7 + 3 ^{39} \cdot 7}{2 ^{38} \cdot 45} = \frac{2 ^{39} \cdot 7}{2 ^{38} \cdot 45} + \frac{3 ^{39} \cdot 7}{2 ^{38} \cdot 45}

= - \frac{14}{27} + \frac{2 ^{39} \cdot 7}{2 ^{38} \cdot 45} + \frac{3 ^{39} \cdot 7}{2 ^{38} \cdot 45}

\frac{2 ^{39} \cdot 7}{2 ^{38} \cdot 45} = \frac{14}{45}

\frac{3 ^{39} \cdot 7}{2 ^{38} \cdot 45} = \frac{3 ^{37} \cdot 7}{2 ^{38} \cdot 5}

= - \frac{14}{27} + \frac{14}{45} + \frac{3 ^{37} \cdot 7}{2 ^{38} \cdot 5}

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What is expand-14/27+(7(2^{39}+3^{39}))/(2^{38)*45} ?
The solution to expand-14/27+(7(2^{39}+3^{39}))/(2^{38)*45} is -14/27+14/45+(3^{37}*7)/(2^{38)*5}