Question

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Answer 1

Step-by-step explanation:

First of all, remember these points-

• Whenever there is a (-) sign in the Power, transfer it to denominator.
• Look out for readymate answers (roots, already cubed numbers)

We have :-

$\tt{ \dfrac{6^{-2} \times 2 ^ {-3} \times (729)^{\dfrac{2}{3}}}{ (125)^{ \dfrac{-1}{3}} \times (64)^{\dfrac{-1}{6}}}}$

We can do the following:-

• Transfer 6-² to denominator
• Write 729 as 9³
• Write 125 as 5³
• Write 64 as 2⁶

We transferred 6² to denominator and 2³ as well.

What we get after these simplification is some powers get cut (729, 125, 64)

Now refer to attachment :-

The answer is 15/4 (Filtered image due to sunlight)

Answer 2

Required Amswer :-

$\sf \dfrac{6^{-2}\times 2^{-3}\times 729^{\dfrac{-2}{3}}}{(125)^{\dfrac{-1}{3}} \times 64^{\dfrac{-1}{6}}}$

$\sf \dfrac{9^{3\times\frac{2}{3}}}{6^2\times 2^3\times 5^{3\times\frac{-1}{3}}\times 2^{6\times\frac{-1}{6}}}$

$\sf \dfrac{9^{2}}{6^2\times 2^3\times 5^{-1} \times 2^{-1}}$

$\sf\dfrac{81}{6^2\times 5^{-1}\times 2^{3+(-1)}}$

$\sf\dfrac{81}{6^2 \times 5^{-1}\times 2^{3-1}}$

$\sf\dfrac{81}{36 \times 5^{-1}\times 2^{2}}$

$\sf\dfrac{81}{36\times 4\times 5^{-1}}$

$\sf\dfrac{81}{\dfrac{144}{5}}$

$\sf\dfrac{81}{144}\times 5$

$\sf\dfrac{405}{144}$

$\sf \dfrac{15}{4} =3 \dfrac{3}{4}$