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11111nata11111 [884]
2 years ago
8

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

Mathematics
1 answer:
vodka [1.7K]2 years ago
8 0

Answer:

The powers are 3 and 5.

Step-by-step 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.

   

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