Question

প্রমাণ কর যে: $\frac{a^{p+q}}{a^{2r}}\times\frac{a^{q+r}}{a^{2p}}\times\frac{a^{r+p}}{a^{2q}}=1$

Answer 1

Left Hand Side,
$\frac{a^{p+q}}{a^{2r}}\times\frac{a^{q+r}}{a^{2p}}\times\frac{a^{r+p}}{a^{2q}}$

$=a^{p+q-2r}\times a^{q+r-2p}\times a^{r+p-2q}$

$=a^{\left(p+q-2r\right)+\left(^{q+r-2p}\right)+\left(r+p-2q\right)}$

$=a^{p+q-2r+^{q+r-2p}+r+p-2q}$

$=a^0$

$=1$

$=$ Right Hand Side [Proved]

Comments

Rules Applied:

• $\frac{a^{m}}{a^{n}}=a^{m-n}$
• $a^{m} \cdot a^{n}=a^{m+n}$
• $a^{0}=1$