Question

x^m+n×x^n+l×x^l+m÷(x^m×x^n×x^l)^2

Answer 1

Answer:

( x^{l} / x^{m}) ^{1/lm}. ( x^{m} / x^{n}) ^{1/mn}. ( x^{n} / x^{l}) ^{1/nl}(x

l

/x

m

)

1/lm

.(x

m

/x

n

)

1/mn

.(x

n

/x

l

)

1/nl

=( x^{l-m} ) ^{1/lm}. ( x^{m-n} ) ^{1/mn}. ( x^{n-l}) ^{1/nl}(x

l−m

)

1/lm

.(x

m−n

)

1/mn

.(x

n−l

)

1/nl

=x^{(l-m)/lm}. x^{(m-n)/mn}. x^{(n-l)/nl}x

(l−m)/lm

.x

(m−n)/mn

.x

(n−l)/nl

=x^{(l-m)/lm+(m-n)/mn+(n-l)/nl}x

(l−m)/lm+(m−n)/mn+(n−l)/nl

=x^{(ln-mn+lm-ln+mn-lm)/lmn}x

(ln−mn+lm−ln+mn−lm)/lmn

=x^{0}x

0

=1 (Proved)

Step-by-step explanation:

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Answer 2

$\huge\boxed{\underline{\underline{\green{Solution}}}}$

$\displaystyle \: \frac{ {x}^{(m + n) } \times {x}^{(n + l)} \times {x}^{(l + m) } }{ {( {x}^{m} \times {x}^{n} \times {x}^{l} ) }^{2} }$

$= \displaystyle \: \frac{ {x}^{(m + n + n + l + l + m) } }{ {( {x}^{m + n + l} ) }^{2} }$

$= \displaystyle \: \frac{ {x}^{(2m + 2n + 2l ) } }{ { {x}^{(2m + 2n +2 l) } } }$

$= 1$

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