49
and
16
81 me yfjysrgutfhghfg of the day and I'm a bit concerned
Answers
Answer:
The simplified form of the given expression is \dfrac{63}{2}
2
63
.
Step-by-step explanation:
The given expression is
(\frac{16}{81})^{-\frac{3}{4}}\times (\frac{49}{9})^{\frac{3}{2}}\div (\frac{343}{216})^{\frac{2}{3}}(
81
16
)
−
4
3
×(
9
49
)
2
3
÷(
216
343
)
3
2
It can be rewritten as
((\frac{2}{3})^4)^{-\frac{3}{4}}\times ((\frac{7}{3})^2)^{\frac{3}{2}}\div ((\frac{7}{6})^3)^{\frac{2}{3}}((
3
2
)
4
)
−
4
3
×((
3
7
)
2
)
2
3
÷((
6
7
)
3
)
3
2
Using exponential property we get
(\frac{2}{3})^{-3}\times (\frac{7}{3})^{3}\div (\frac{7}{6})^{2}(
3
2
)
−3
×(
3
7
)
3
÷(
6
7
)
2
[\because (a^m)^n=a^{mn}][∵(a
m
)
n
=a
mn
]
(\frac{3}{2})^{3}\times (\frac{7}{3})^{3}\div (\frac{7}{6})^{2}(
2
3
)
3
×(
3
7
)
3
÷(
6
7
)
2
[\because (a)^n=(\frac{1}{a})^{-n}][∵(a)
n
=(
a
1
)
−n
]
\frac{27}{8}\times \frac{343}{27}\div (\frac{49}{36})
8
27
×
27
343
÷(
36
49
)
\frac{27}{8}\times \frac{343}{8}\times \frac{36}{49}
8
27
×
8
343
×
49
36
\frac{63}{2}
2
63
Therefore, the value of given expression is \frac{63}{2}
2
63
.
