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What is the value of 4^{10} * 8^{20} * 16^{5}? Express your answer in the form a^b, where a and b are positive integers such that a is the least possible positive integer.

 May 4, 2022

Best Answer 

 #1
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+2

You can write like this:

 

4^10 ==(2^2)^10 ==2^20 [you multiply the exponents: 2 * 10 ==20]

 

8^20 ==(2^3)^20 ==2^60 [same as above]

 

16^5 ==(2^4)^5 ==2^20 [same as above.

 

Now that we the base for all of them, which is 2, then we can multiply them as follows:

 

[2^20  x  2^60  x  2^20] ==2^(20 + 60 + 20) ==2^100 [When the base is the same, you ADD the exponents when multiplying them together].

 May 4, 2022
 #1
avatar
+2
Best Answer

You can write like this:

 

4^10 ==(2^2)^10 ==2^20 [you multiply the exponents: 2 * 10 ==20]

 

8^20 ==(2^3)^20 ==2^60 [same as above]

 

16^5 ==(2^4)^5 ==2^20 [same as above.

 

Now that we the base for all of them, which is 2, then we can multiply them as follows:

 

[2^20  x  2^60  x  2^20] ==2^(20 + 60 + 20) ==2^100 [When the base is the same, you ADD the exponents when multiplying them together].

Guest May 4, 2022

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