3-¹ + 3-² = 1)1/4 2)1/3 3)5/4 4)4/9
Answers
Answer:
(
3
2
)
2
}
3
×(
3
1
)
−4
×3
−1
×(
6
1
)]=
81
32
Step-by-step explanation:
Given : Expression [\{(\frac{2}{3})^2\}^3\times (\frac{1}{3})^{-4}\times 3^{-1}\times (\frac{1}{6})][{(
3
2
)
2
}
3
×(
3
1
)
−4
×3
−1
×(
6
1
)]
To find : Simplify the expression ?
Solution :
Solving the expression,
[\{(\frac{2}{3})^2\}^3\times (\frac{1}{3})^{-4}\times 3^{-1}\times (\frac{1}{6})][{(
3
2
)
2
}
3
×(
3
1
)
−4
×3
−1
×(
6
1
)]
=[\{(\frac{4}{9})\}^3\times (3)^{4}\times\frac{1}{3} \times (\frac{1}{6})]=[{(
9
4
)}
3
×(3)
4
×
3
1
×(
6
1
)]
=[\frac{64}{729}\times 81\times\frac{1}{3} \times \frac{1}{6}]=[
729
64
×81×
3
1
×
6
1
]
=\frac{32}{81}=
81
32
Therefore, [\{(\frac{2}{3})^2\}^3\times (\frac{1}{3})^{-4}\times 3^{-1}\times (\frac{1}{6})]=\frac{32}{81}[{(
3
2
)
2
}
3
×(
3
1
)
−4
×3
−1
×(
6
1
)]=
81
32