Question

simplify (p/q)^k * (q/r)^k+2 * (r/p)^k-1 ,for k=2

Answer 1

Solution:-

$\bf \:( \frac{p}{q} ) {}^{k} \times ( \frac{q}{r} ) {}^{k + 2} \times ( \frac{r}{p} ) {}^{k - 1}$

In wich value of k = 2

So put the value of k on given equation

$\bf \:( \frac{p}{q} ) {}^{2} \times ( \frac{q}{r} ) {}^{2 + 2} \times ( \frac{r}{p} ) {}^{2 - 1}$

$\bf \:( \frac{p}{q} ) {}^{2} \times ( \frac{q}{r} ) {}^{4} \times ( \frac{r}{p} ) {}^{1}$

$\bf \: \frac{p {}^{2} }{q {}^{2} } \times \frac{q {}^{4} }{r {}^{4} } \times \frac{r}{p}$

Now we write

$\bf \: \frac{p \times p \times q \times q \times q \times q \times r}{q \times q \times r \times r \times r \times r \times p}$

$\bf \: \frac{ \not \: p \times p \times \not \: q \times \not q \times q \times q \times \not r}{ \not \: q \times \not \: q \times \not r \times r \times r \times r \times \not p}$

$\to \bf \: \frac{pq {}^{2} }{ {r}^{3} }$

$\boxed{ \green{ \large \: \bf \: answer = \bf \: \frac{pq {}^{2} }{ {r}^{3} } }}$

Answer 2

Answer.

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