Question

(16/18)^-3/4

Answer 1

\(\bf a^{-{\color{red} n}} = \cfrac{1}{a^{\color{red} n}}\qquad thus\quad \large \left(\cfrac{16}{18}\right)^{-{\color{red}{ \frac{3}{4}}}}\implies ?\)

Answer 2

same as
\[\large\left(\frac{8}{9}\right)^{-\frac{3}{4}}\] or
\[\large \left(\frac{9}{8}\right)^{\frac{3}{4}}\]

Answer 3

Thank you very much, this was very helpful!

Answer 4

I am still having trouble though. The problem states: "evaluate the expression without using calculator". I have the answer but it is not making any sense. the answer is 27/8. Could someone explain this to me?

Answer 5

aah i see
you must have made a typo in the question

Answer 6

\[\large\left(\frac{16}{81}\right)^{-\frac{3}{4}}\] i bet

Answer 7

not \(18\)

Answer 8

then the answer would be what you said

Answer 9

please tell me i am right

Answer 10

Yeah that was my typo my bad. Now It makes a bit more sense.

Answer 11

once you flip and get
\[\large\left(\frac{81}{16}\right)^{\frac{3}{4}}\] the four in the denominator of the exponent means take the fourth root
the fourth root of 81 is 3
the fourth root of 16 is 2
\[\left(\frac{3}{2}\right)^3=\frac{27}{8}\]

Answer 12

Thank you very much. It all makes sense now!