(3 ^ - 1 + 4 ^ - 1) ^ - 1 / (5 ^ - 1)
Answers
Correct option is
B
7
60
Given (3
−1
+4
−1
)
−1
÷5
−1
We know according to the law of exponents a
−m
=(
a
m
1
)
consider (3)
−1
We can write given equation as 3
−1
=(
3
1
1
)
substituting in above we get (3)
−1
=
3
1
We know according to the law of exponents a
−m
=(
a
m
1
)
consider (4)
−1
We can write given equation as (4)
−1
=(
4
1
)
We know according to the law of exponents a
−m
=(
a
m
1
)
consider (5)
−1
We can write given equation as 5
−1
=(
5
1
)
Now substituting all above values in question we get
(3
−1
+4
−1
)
−1
÷5
−1
=[(
3
1
)+(
4
1
)]
−1
÷(
5
1
)
Now by taking the LCM we can have [∴ LCM of 3 and 4 is 12]
[(
3
1
)+(
4
1
)]
−1
÷(
5
1
)=[(
12
4+3
)]
−1
÷(
5
1
)
⇒[(
12
4+3
)]
−1
÷(
5
1
)=[(
12
7
)]
−1
÷(
5
1
)
We know according to the law of exponents a
−m
=(
a
m
1
)
⇒[(
12
7
)]
−1
÷(
5
1
)
On simplifying we get
⇒[(
7
12
)]
1
÷(
5
1
)
⇒(
7
12
)×(
1
5
)
=
7
60