Question

প্রমাণ কর যে: $\left(\frac{a^{l}}{a^{m}}\right)^{n}\cdot\left(\frac{a^{m}}{a^{n}}\right)^{l}\cdot\left(\frac{a^{n}}{a^{l}}\right)^{m}=1$

Answer 1

Left Hand Side,
$\left(\frac{a^{l}}{a^{m}}\right)^{n}\cdot\left(\frac{a^{m}}{a^{n}}\right)^{l}\cdot\left(\frac{a^{n}}{a^{l}}\right)^{m}$

$=\frac{a^{ln}}{a^{mn}}\cdot\frac{a^{lm}}{a^{ln}}\cdot\frac{a^{mn}}{a^{lm}}^{}$

$=a^{ln-mn}\cdot a^{lm-ln}\cdot a^{mn-lm}$

$=a^{ln-mn+lm-ln+mn-lm}$

$=a^0$

$=1$

$=$ Right Hand Side [Proved]

Comments

Rules Applied:

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