Question

find the value of (16/81)power -3/4

Answer 1

here is your answer
hope it will help you don't forget to follow and please make it brainliest answer

Answer 2

We have:

$(\dfrac{16}{81})^{\dfrac{-3}{4}}$

We have to find, the value of $(\dfrac{16}{81})^{\dfrac{-3}{4}}$ = ?

Solution:

∴ $(\dfrac{16}{81})^{\dfrac{-3}{4}}$

16 = 2 × 2 × 2 × 2 = $2^4$ and

81 = 3 × 3 × 3 × 3 = $3^4$

= $(\dfrac{2^4}{3^4})^{\dfrac{-3}{4}}$

= $(\dfrac{2}{3}^4)^{\dfrac{-3}{4}}$ [ ∵ $\dfrac{a^m}{b^m} =(\dfrac{a}{b})^m$ ]

= $(\dfrac{2}{3})^{4\times {\dfrac{-3}{4}}$ [ ∵ $a^{m} ^n=a^{mn}$]

= $(\dfrac{2}{3})^{-3}$

= $(\dfrac{3}{2})^{3}$ [ ∵ $(\dfrac{a}{b})^{-m}=(\dfrac{b}{a})^{m}$]

= $\dfrac{3\times 3 \times 3}{2\times 2 \times 2}$

= $\dfrac{27}{8}$

∴ $(\dfrac{16}{81})^{\dfrac{-3}{4}}$ = $\dfrac{27}{8}$

Thus, the value of $(\dfrac{16}{81})^{\dfrac{-3}{4}}$ is "equal to $\dfrac{27}{8}$".