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The product of two powers is 11^8 and their quotient is 11². What are the two powers? Explain.

User Lordzuko
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1 Answer

26 votes
26 votes

Answer:

The powers are 3 and 5.

Explanation:

When you multiply 2 exponential functions you add the powers and when you divide these functions you subtract the powers, so we have:

11^a * 11^b = 11^(a+b)

11^a/ 11^b = 11^(a-b)

So, from the information given:

a + b = 8

a - b = 2 Adding:-

2a = 10

a = 5.

and substituting in the second equation

5 - b = 2

b = 3.

User Titicaca
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