((49) ^ (3/2) - (49) ^ (5/2))/(49 ^ (3/2))
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18
Answer:
Consider the given expression is
(49)^{\frac{3}{2}}-\dfrac{49^{\frac{5}{2}}}{49}(49)
2
3
−
49
49
2
5
In the above expression 49 can be written as 7^27
2
.
(7^2)^{\frac{3}{2}}-\dfrac{(7^2)^{\frac{5}{2}}}{7^2}(7
2
)
2
3
−
7
2
(7
2
)
2
5
Using the properties of exponents we get
7^3-\dfrac{7^5}{7^2}7
3
−
7
2
7
5
[\because (a^m)^n=a^{mn}][∵(a
m
)
n
=a
mn
]
7^3-7^{5-2}7
3
−7
5−2
[\because \dfrac{a^m}{a^n}=a^{m-n}][∵
a
n
a
m
=a
m−n
]
7^3-7^{3}7
3
−7
3
00
Therefore value of given expression is 0.
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