Set up the term

First, you need to "translate" the text in the task into a mathematical term:

Now you put this together to a term.

If you write the division with the divide-by sign, you get:

$6^4:(9\cdot 16)6^4\; :\; (9\backslash cdot\; 16)$

(Important: Around "$9\cdot 169\backslash cdot16$" you have to write a parenthesis, because otherwise it would be divided only by $99$ and not by $9\cdot 169\backslash cdot\; 16$).

If you write the division with the fraction bar, you get:

${\displaystyle \frac{6^4}{9\cdot 16}}\backslash dfrac\{6^4\}\{9\backslash cdot16\}$

(You don't need to put parentheses here because the fraction bar acts like a parenthesis).

Calculate term

1st way:

Now calculate the term:

${\displaystyle \frac{6^4}{9\cdot 16}}\backslash dfrac\{6^4\}\{9\backslash cdot16\}$$={\displaystyle \frac{1296}{144}}=\backslash dfrac\{1296\}\{144\}$

Since 1296 is a multiple of 144, you can shorten the fraction by 144.

${\displaystyle \frac{6^4}{9\cdot 16}}={\displaystyle \frac{1296}{144}}=9\backslash dfrac\{6^4\}\{9\backslash cdot\; 16\}=\; \backslash dfrac\{1296\}\{144\}=9$

2nd way:

${\displaystyle \frac{6^4}{9\cdot 16}}={\displaystyle \frac{(2\cdot 3{)}^4}{3^2\cdot 2^4}}\backslash dfrac\{6^4\}\{9\backslash cdot16\}\backslash \; =\backslash \; \backslash dfrac\{(2\backslash cdot3)^4\}\{3^2\backslash cdot2^4\}$

${\displaystyle \frac{2^4\cdot 3^4}{3^2\cdot 2^4}}={\displaystyle \frac{\cancel{2^4}\cdot 3^4}{3^2\cdot \cancel{2^4}}}={\displaystyle \frac{3^4}{3^2}}=3^{(4-2)}\backslash dfrac\{\; 2^4\backslash cdot3^4\}\{3^2\backslash cdot2^4\}\backslash \; =\backslash \; \backslash dfrac\{\backslash cancel\; \{2^4\}\backslash cdot3^4\}\{3^2\backslash cdot\backslash cancel\{2^4\}\}\backslash \; =\backslash \; \backslash dfrac\{3^4\}\{3^2\}\backslash \; =\backslash \; 3^\{(4-2)\}$ apply the power laws

$3^2=93^2\backslash \; =\backslash \; 9$