Question

The value of (3/4)^-4 × (2/3)^5
​

Answer 1

$\huge\boxed{\fcolorbox{red}{pink}{Answer:-}}$

$\mathtt\red{ ({ \frac{3}{4}) }^{- 4} \times ({ \frac{2}{3}) }^{5}} \\ \\ =\mathtt{ ({\frac{4}{3}) }^{4} \times { (\frac{2}{3}) }^{5}} \\ \\ =\mathtt{ \frac{4 \times 4 \times 4 \times 4}{3 \times 3 \times 3 \times 3} \times \frac{2 \times 2 \times 2 \times 2 \times 2}{3 \times 3 \times 3 \times 3 \times 3} } \\ \\ =\mathtt{ \frac{256}{81} \times \frac{32}{243} } \\ \\ = \mathtt{ \frac{8192}{19683}\:\:or\:\:0.416197 }$

Answer 2

Answer:

Answer:-

\begin{gathered} \mathtt\red{ ({ \frac{3}{4}) }^{- 4} \times ({ \frac{2}{3}) }^{5}} \\ \\ =\mathtt{ ({\frac{4}{3}) }^{4} \times { (\frac{2}{3}) }^{5}} \\ \\ =\mathtt{ \frac{4 \times 4 \times 4 \times 4}{3 \times 3 \times 3 \times 3} \times \frac{2 \times 2 \times 2 \times 2 \times 2}{3 \times 3 \times 3 \times 3 \times 3} } \\ \\ =\mathtt{ \frac{256}{81} \times \frac{32}{243} } \\ \\ = \mathtt{ \frac{8192}{19683}\:\:or\:\:0.416197 } \end{gathered}

(

4

3

)

−4

×(

3

2

)

5

=(

3

4

)

4

×(

3

2

)

5

=

3×3×3×3

4×4×4×4

×

3×3×3×3×3

2×2×2×2×2

=

81

256

×

243

32

=

19683

8192

or0.416197