Solve 0.651-1/1.063^5/0.063+101/1.063^5

$$0.65 \frac{ 1- \frac{ 1 }{ { 1.063 }^{ 5 } } }{ 0.063 } +10 \frac{ 1 }{ { 1.063 }^{ 5 } }$$

Evaluate

$$\frac{13686121392174650}{1357270227241543}\approx 10.08356414$$

Solution Steps

Calculate 1.063 to the power of 5 and get 1.357270227241543.

$$0.65\times \frac{1-\frac{1}{1.357270227241543}}{0.063}+10\times \frac{1}{1.063^{5}}$$

Expand \frac{1}{1.357270227241543} by multiplying both numerator and the denominator by 1000000000000000.

$$0.65\times \frac{1-\frac{1000000000000000}{1357270227241543}}{0.063}+10\times \frac{1}{1.063^{5}}$$

Convert 1 to fraction \frac{1357270227241543}{1357270227241543}.

$$0.65\times \frac{\frac{1357270227241543}{1357270227241543}-\frac{1000000000000000}{1357270227241543}}{0.063}+10\times \frac{1}{1.063^{5}}$$

Since \frac{1357270227241543}{1357270227241543} and \frac{1000000000000000}{1357270227241543} have the same denominator, subtract them by subtracting their numerators.

$$0.65\times \frac{\frac{1357270227241543-1000000000000000}{1357270227241543}}{0.063}+10\times \frac{1}{1.063^{5}}$$

Subtract 1000000000000000 from 1357270227241543 to get 357270227241543.

$$0.65\times \frac{\frac{357270227241543}{1357270227241543}}{0.063}+10\times \frac{1}{1.063^{5}}$$

Express \frac{\frac{357270227241543}{1357270227241543}}{0.063} as a single fraction.

$$0.65\times \frac{357270227241543}{1357270227241543\times 0.063}+10\times \frac{1}{1.063^{5}}$$

Multiply 1357270227241543 and 0.063 to get 85508024316217.209.

$$0.65\times \frac{357270227241543}{85508024316217.209}+10\times \frac{1}{1.063^{5}}$$

Expand \frac{357270227241543}{85508024316217.209} by multiplying both numerator and the denominator by 1000.

$$0.65\times \frac{357270227241543000}{85508024316217209}+10\times \frac{1}{1.063^{5}}$$

Reduce the fraction \frac{357270227241543000}{85508024316217209} to lowest terms by extracting and canceling out 63.

$$0.65\times \frac{5670955987961000}{1357270227241543}+10\times \frac{1}{1.063^{5}}$$

Convert decimal number 0.65 to fraction \frac{65}{100}. Reduce the fraction \frac{65}{100} to lowest terms by extracting and canceling out 5.

$$\frac{13}{20}\times \frac{5670955987961000}{1357270227241543}+10\times \frac{1}{1.063^{5}}$$

Multiply \frac{13}{20} times \frac{5670955987961000}{1357270227241543} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 5670955987961000}{20\times 1357270227241543}+10\times \frac{1}{1.063^{5}}$$

Do the multiplications in the fraction \frac{13\times 5670955987961000}{20\times 1357270227241543}.

$$\frac{73722427843493000}{27145404544830860}+10\times \frac{1}{1.063^{5}}$$

Reduce the fraction \frac{73722427843493000}{27145404544830860} to lowest terms by extracting and canceling out 20.

$$\frac{3686121392174650}{1357270227241543}+10\times \frac{1}{1.063^{5}}$$

Calculate 1.063 to the power of 5 and get 1.357270227241543.

$$\frac{3686121392174650}{1357270227241543}+10\times \frac{1}{1.357270227241543}$$

Expand \frac{1}{1.357270227241543} by multiplying both numerator and the denominator by 1000000000000000.

$$\frac{3686121392174650}{1357270227241543}+10\times \frac{1000000000000000}{1357270227241543}$$

Express 10\times \frac{1000000000000000}{1357270227241543} as a single fraction.

$$\frac{3686121392174650}{1357270227241543}+\frac{10\times 1000000000000000}{1357270227241543}$$

Multiply 10 and 1000000000000000 to get 10000000000000000.

$$\frac{3686121392174650}{1357270227241543}+\frac{10000000000000000}{1357270227241543}$$

Since \frac{3686121392174650}{1357270227241543} and \frac{10000000000000000}{1357270227241543} have the same denominator, add them by adding their numerators.

$$\frac{3686121392174650+10000000000000000}{1357270227241543}$$

Add 3686121392174650 and 10000000000000000 to get 13686121392174650.

$$\frac{13686121392174650}{1357270227241543}$$

Factor

$$\frac{2 \cdot 421 \cdot 650172037633 \cdot 5 ^ {2}}{1063 ^ {5}} = 10\frac{113419119759220}{1357270227241543} = 10.083564140347887$$