Question

Given a+b=7 and a–b=3, find: 3^a÷3^b

Answer 1

Answer:

27

Step-by-step explanation:

a + b = 7 ...( 1 )

a - b = 3 ...( 2 )

Adding both equations :

= > a + b + a - b = 7 + 3

= > 2a = 10

= > a = 5

Hence,

a - b = 3

= > 5 - b = 3

= > 5 - 3 = b = 2

Thus,

3^a / 3^b

= > 3^5 / 3^2

= > 243 / 9

= > 27

This could also be solved using the properties of exponents ; 3^a / 3^b => 3^( a - b ) => 3^3 => 27

Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

a + b = 7 and a - b = 3.

To Find:

3^a / 3^b

Solution:

a + b = 7______(1)

a - b = 3______(2)

On adding both the equations we get,

a + b + a - b = 7 + 3

2a = 10

a = 10/2

a = 5

Substituting the value of a in equation 1 we get,

5 + b = 7

or b = 7 - 5

=> b = 2

Now, 3^a / 3^b = 3^5 / 3^2

= 243/9

= 27

Hence, the value of 3^a / 3^b is 27.