Pls answer the question from Number systems class 9th

1.	Pls answer the question from Number systems class 9th
Answer» 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.

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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:

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

Use these laws to prove the statement GIVEN.

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