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If ab = 53,...

Question

If $\frac{a}{b} = \frac{5}{3},$ then find the value of $\frac{a^{3} - b^{3}}{b^{3}} .$

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Solution

Given,
$\frac{a}{b} = \frac{5}{3},$ .....(1).
Then,
$\frac{a^{3} - b^{3}}{b^{3}}$
$= {(\frac{a}{b})}^{3} - 1$
$= \frac{5^{3}}{3^{3}} - 1$ [ Using (1)]
$= \frac{125 - 27}{27}$
$= \frac{98}{27}$ .

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