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List three different ways to write 5^11 as the product of two powers. Explain why all three of your expressions are equal to 5^11

User Abdu
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In multiplying quantities of the same base, the product is simply the base raised to a power that is the sum of the individual powers of the factors. That is,
(a^n)(a^m)= a^(n+m)

The term
5^(11) can be expressed as the product of two factors with the same base (which is five) and whose powers add up to 11. Three examples are:

(5^1)(5^(10)) = 5^(1+10) = 5^(11) \\ (5^5)(5^6) = 5^(5+6) = 5^(11) \\ (5^8)(5^3) = 5^(8+3) = 5^(11)
User Harsel
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