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notsponge [240]
3 years ago
13

Given a+b=7 and a–b=3, find: 2^a·2^b

Mathematics
1 answer:
Semmy [17]3 years ago
8 0

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.

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