Question

Given a+b=7 and a–b=3, find: 2^a·2^b

Answer 1

Explanation:

`a + b = 7 .....(1)\\ a - b = 3.....(2) \\ (1) + (2) = > 2a - 0b = 10 \\ 2a = 10 \\ a = 5......(3) \\ put \: (3)in \: (1) \\ then \:5 + b = 7 \\ b = 2 \\ then \: {2}^(a) * {2}^(b) \\ = {2}^(5) * {2}^(2) \\ = 32 * 4 \\ = 128 \\ thank \: you`

Answer 2

a +b = 7

a-b = 3

Rewrite the second equation as a = 3+b

Replace a in the first equation with that:

3+b + b = 7

Simplify:

3 +2b = 7

Subtract 3 from both sides:

2b = 4

Divide both sides by 2:

b = 4/2 = 2

Now replace b in the first equation with 2 to solve for a:

a + 2 =7

a = 7-2 = 5

so you now have a and b.

Now solve the given equation:

2^a * 2^b

2^5 * 2^2

32*4

128

The answer is 128.