Question

in this problem: (4/9)^2 ÷ (4/9)^3 why is the answer 9/4^-1 instead of 4/9^-1 ? please explain am I missing something​

Answer 1

Answer:

$( \frac{4}{9} )^{2} \div ( \frac{ 4}{9} ) ^{3}$

we know

${a}^{m} \div {a}^{n} = {a}^{m - n}$

same rule applicable here

that is

$(\frac{4}{9} )^{2 - 3} \\( \frac{4}{9} ) ^{ - 1}$

we know

$( { \frac{a}{b} })^{ - n} \\ = (\frac{b}{a} ) ^{n}$

we've to take reciprocal and remove negative sign from the power

that is

${( \frac{4}{9}) }^{ - 1} \\ = (\frac{9}{4}) ^{1} \\ \frac{9}{4}$

that's why the answer is 9/4

hope it helps

Answer 2

Answer:

because in dvision right side became Reciprocal

that mulitly so power become negative