Solve for: (150000(1-1.1^5))/(1-1.1)

Expression: $\frac{ 150000\left( 1-{1.1}^{5} \right) }{ 1-1.1 }$

Convert the decimal into a fraction

$\frac{ 150000\left( 1-{\left( \frac{ 11 }{ 10 } \right)}^{5} \right) }{ 1-1.1 }$

Calculate the difference

$\frac{ 150000\left( 1-{\left( \frac{ 11 }{ 10 } \right)}^{5} \right) }{ -0.1 }$

To raise a fraction to a power, raise the numerator and denominator to that power

$\frac{ 150000\left( 1-\frac{ {11}^{5} }{ {10}^{5} } \right) }{ -0.1 }$

Convert the decimal into a fraction

$\frac{ 150000\left( 1-\frac{ {11}^{5} }{ {10}^{5} } \right) }{ -\frac{ 1 }{ 10 } }$

Distribute $150000$ through the parentheses

$\frac{ 150000-\frac{ 3 \times {11}^{5} }{ 2 } }{ -\frac{ 1 }{ 10 } }$

Write all numerators above the common denominator

$\frac{ \frac{ 300000-3 \times {11}^{5} }{ 2 } }{ -\frac{ 1 }{ 10 } }$

Use $\frac{ -a }{ b }=\frac{ a }{ -b }=-\frac{ a }{ b }$ to rewrite the fraction

$-\frac{ \frac{ 300000-3 \times {11}^{5} }{ 2 } }{ \frac{ 1 }{ 10 } }$

Simplify the complex fraction

$-\left( 300000-3 \times {11}^{5} \right) \times 5$

Distribute $5$ through the parentheses

$-\left( 1500000-15 \times {11}^{5} \right)$

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

$\begin{align*}&-1500000+15 \times {11}^{5} \\&915765\end{align*}$