list three different ways to write 5^11 as of two powers. explain why all three of of your expressions are equal to 5^11
1) (5^5)^2 x 5 = 5^10 x 5 = 5^11
We can break down 5^11 into (5^5)^2 x 5, which is equal to 5^10 x 5. This is because when we multiply two exponents with the same base, we add their powers.
2) (5^3)^3 x 5^2 = 5^9 x 5^2 = 5^11
We can also break down 5^11 into (5^3)^3 x 5^2. This is because when we have multiple exponents with the same base, we can add their powers and keep the same base.
3) 5^10 x 5^1 = 5^11
Lastly, we can simply write 5^11 as 5^10 x 5^1. This is because when we multiply two exponents with the same base, we add their powers.
All three expressions are equal to 5^11 because they all represent the same base (5) raised to the same power (11). The order in which we multiply, break down, and write the exponents does not affect the final result.