1 -: by what number we should multiply 4 - 8 so that the product may be equal to 4 ?
2-: by what number 5 6 be divided so that the quotient maybe equal to 5 - 2 .
please give the answer if you know with correct in explanation
Answers
Step-by-step explanation:
Solution :-
5)
Given number = 4^-8
Let the required number should be multiplied X
On multiplying 4^-8 with X
=> 4^-8 × X
The result = (4^-8 )X
According to the given problem
The result of the product = 4
=> (4^-8 )X = 4
We know that a^-n = 1/a^n
=> (1/4⁸) X = 4
=> X/4⁸ = 4
=> X = 4×4⁸
=>X = 4¹ × 4⁸
We know that
a^m × a^n = a^(m+n)
=> X = 4^(1+8)
=> X = 4⁹
So , the value of X = 4⁹
The required number is 4⁹
Check:-
The required number is 4⁹
Given number = 4^-8
On multiplying 4^-8 with 4⁹
=> 4⁹×4^-8
=> 4^(9-8)
=>4¹
=> 4
Verified the given relation in the given problem.
6)
Given number = 5⁶
Let the required number be X
On dividing 5⁶ with X
=> 5⁶/X
The result = (5⁶)/X
According to the given problem
The quotient = 5^-2
=> (5⁶)/X= 5^-2
=> X× 5^-2 = 5⁶
=> X = 5⁶/5^-2
We know that
a^m/a^n = a^(m-n)
=> X = 5^(6-(-2))
=>X = 5^(6+2)
=> X = 5⁸
So , the value of X = 5⁸
The required number is 5⁸
Check:-
The required number is 5⁸
Given number = 5⁶
=> On dividing 5⁶ by 5⁸
=> 5⁶/5⁸
We know that
a^m/a^n = a^(m-n)
=>5^(6-8)
=>5^-2
Verified the given relation in the given problem
Used formulae:-
- a^-n = 1/a^n
- a^m × a^n = a^(m+n)
- a^m/a^n = a^(m-n)