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.
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].
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].
