Question

pls answer the question from Number systems
class 9th​

Answer 1

Answer:

Proved that $(\frac{x^{l}}{x^{m}})^\frac{1}{lm} \times (\frac{x^{m}}{x^{m}})^\frac{1}{mn}\times (\frac{x^{n}}{x^{l}})^\frac{1}{nl}=1$.

Step-by-step explanation:

Some laws of exponent are:

• $\frac{a^{m}}{a^{n}}=a^{m-n}$
• $a^{m}\times a^{n}=a^{m+n}$
• $(a^{m})^{n}=a^{mn}$

Use these laws to prove the statement given.

$(\frac{x^{l}}{x^{m}})^\frac{1}{lm} \times (\frac{x^{m}}{x^{m}})^\frac{1}{mn}\times (\frac{x^{n}}{x^{l}})^\frac{1}{nl}=(x^{l-m})^\frac{1}{lm}\times (x^{m-n})^\frac{1}{mn}\times (x^{n-l})^\frac{1}{nl}$

                                            $=x^\frac{l-m}{lm}\times x^\frac{m-n}{mn}\times x^\frac{n-l}{nl}$

                                            $=x^{[\frac{l-m}{lm}+\frac{m-n}{mn}+\frac{n-l}{nl}]}$

                                            $=x^{[\frac{nl-nm+lm-nl+nm-lm}{lmn} ]}$

                                            $=x^{0}\\=1$

Hence proved.