Question

Simplify: (81/16) -3/4 * (25/9) -3/2

Answer 1

If I am not wrong, the question is (81/16)^-3/4*(25/9)^-3/2 which is not mentioned in this question.
Solution:-
(81/16)^-3/4 = {(3/2)^4}^-3/4
⇒ (3/2)^4×-3/4
⇒ (3/2)^-3
⇒ (2/3)^3
= 8/27
And,
(25/9)^-3/2
⇒ {(5/3)^2}^-3/2
⇒(5/3)^2×-3/2
⇒ (5/3)^-3
⇒ (3/5)^3
= 27/125
Therefore,
(81/16)^-3/4*(25/9)^-3/2 = 8/27 × 27/125
= 8/125  Answer.

Answer 2

Step-by-step explanation:

$Hey friend, \\ \\ </p><p>Here \: \: is \: \: the \: \: answer \: \: you \: were \: looking \: \: for: \\ \\ </p><p>\begin{gathered} {( \frac{81}{16} )}^{ - \frac{3}{4} } \times {( \frac{25}{9} )}^{ - \frac{3}{2} } \\ \\ = {( \frac{ {3}^{4} }{ {2}^{4} } })^{ - \frac{3}{4} } \times {( \frac{ {5}^{2} }{ {3}^{2} }) }^{ - \frac{3}{2} } \\ \\ = {( \frac{3}{2}) }^{4 \times - \frac{3}{4} } \times {( \frac{5}{3} )}^{2 \times - \frac{3}{2} } \\ \\ = {( \frac{3}{2} )}^{ - 3} \times {( \frac{5}{3}) }^{ - 3} \\ \\ = {( \frac{2}{3}) }^{3} \times {( \frac{3}{5} )}^{3} \\ \\ = \frac{2 \times 2 \times 2}{3 \times 3 \times 3} \times \frac{3 \times 3 \times 3}{5 \times 5 \times 5} \\ \\ = \frac{2 \times 2 \times 2}{5 \times 5 \times 5} \\ \\ = \frac{8}{125} \end{gathered} \\ \\ </p><p></p><p></p><p>Hope \: \: this \: \: helps!!!$