Question

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 ​

Answer 1

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)