If m/n=(3/2)^-21 ÷ (81/32)^-6 find the value of (m/n)^-1/3
Answers
Answer:
328
Step-by-step explanation:
Assume that the given expression is
4\times 81^{-\frac{1}{2}}\times (81^{\frac{1}{2}}+81^{\frac{3}{2}})4×81
−
2
1
×(81
2
1
+81
2
3
)
Using the power property of exponent.
4\times (81^{\frac{1}{2}})^{-1}\times (81^{\frac{1}{2}}+(81^{\frac{1}{2}})^3)4×(81
2
1
)
−1
×(81
2
1
+(81
2
1
)
3
) [\because a^{mn}=(a^m)^n][∵a
mn
=(a
m
)
n
]
4\times (9)^{-1}\times (9+(9)^3)4×(9)
−1
×(9+(9)
3
)
On further simplification.
4\times (9)^{-1}\times (9+729)4×(9)
−1
×(9+729)
4\times (9)^{-1}\times 7384×(9)
−1
×738
Using the negative power property of exponent.
4\times \frac{1}{9}\times 7384×
9
1
×738 [\because a^{-n}=\frac{1}{a^n}][∵a
−n
=
a
n
1
]
Cancel out the common factors.
4\times 824×82
328328
Therefore, the value of given expression is 328.