Question

55 points.Please simplify it .Don't answer of your don't know.​

Answer 1

Step-by-step explanation:

i) answer =1

ii) 2 -3m + 6n -2 x 3 3-m

Answer 2

Answer:

( i ) $\boxed{1}$

( ii ) $\boxed{2^{6n - 3m - 2}\times 3^{3 - m}}$

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Step-by-step explanation:

( Part i )

$\left(\frac{1}{x^{a - b}} \right)^{a + b}\left(\frac{1}{x^{b + a}} \right)^{b - a}$

$= \left(\frac{1}{x^{(a - b)(a + b)}} \right)\left(\frac{1}{x^{(b + a)(b - a)}} \right)$

$= \left(\frac{1}{x^{a^2 - b^2}} \right)\left(\frac{1}{x^{b^2-a^2}} \right)$

$= \frac{1}{x^{a^2 - b^2 + (b^2 - a^2)}}$

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

$= \frac{1}{1}$

$= \boxed{1}$

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( Part ii )

$\frac{2^{m + n}\times 3^{2m + 3} \times 4^{2n -1}}{6^{2m + n}\times 12^{m - n}}$

$=\frac{2^{m + n}\times 3^{2m + 3} \times 2^{2(2n -1)}}{(2\times3)^{2m + n}\times (3\times 2^2)^{m - n}}$

$=\frac{2^{m + n}\times 3^{2m + 3} \times 2^{4n -2}}{2^{2m + n}\times3^{2m + n}\times 3^{m - n}\times 2^{2(m - n)}}$

$=\frac{2^{m + n + 4n - 2}\times 3^{2m + 3}}{2^{2m + n + 2m - 2n}\times3^{2m + n + m - n}}$

$=\frac{2^{m + 5n - 2}\times 3^{2m + 3}}{2^{4m - n}\times3^{3m}}$

$= 2^{m + 5n - 2 - (4m - n)}\times3^{2m + 3 - 3m}$

$= \boxed{2^{6n - 3m - 2}\times 3^{3 - m}}$

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Happy to help :)