Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{ { 5 }^{ n+3 } }{ 9 \times { 5 }^{ n } } \frac{ - }{ - } \frac{ { 6.5 }^{ n+1 } }{ 4 \times { 5 }^{ n } }$$

Answer

$$(125*6.5^(n+1))/(36*5^n)$$

Solution


Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[\frac{{5}^{n+3-n}}{9}\times \frac{-}{-}\times \frac{{6.5}^{n+1}}{4\times {5}^{n}}\]
Collect like terms.
\[\frac{{5}^{(n-n)+3}}{9}\times \frac{-}{-}\times \frac{{6.5}^{n+1}}{4\times {5}^{n}}\]
Simplify  \((n-n)+3\)  to  \(3\).
\[\frac{{5}^{3}}{9}\times \frac{-}{-}\times \frac{{6.5}^{n+1}}{4\times {5}^{n}}\]
Simplify  \({5}^{3}\)  to  \(125\).
\[\frac{125}{9}\times \frac{-}{-}\times \frac{{6.5}^{n+1}}{4\times {5}^{n}}\]
Cancel \(-\).
\[\frac{125}{9}\times \frac{{6.5}^{n+1}}{4\times {5}^{n}}\]
Simplify.
\[\frac{125\times {6.5}^{n+1}}{36\times {5}^{n}}\]
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