Question

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

Answer 1

can you put the anwsers all together

Answer 2

1. 5^5 x 5^6: This expression breaks down 5^11 into 5 multiplied by itself 5 times (5^5) and then multiplied by itself 6 more times (5^6).
2. 5^10 x 5^1: This expression breaks down 5^11 into 5 multiplied by itself 10 times (5^10) and then multiplied by itself one more time (5^1).
3. (5^3)^3 x 5^2: This expression breaks down 5^11 into 5 multiplied by itself 3 times, and then that result multiplied by itself 3 times (5^3)^3, and then multiplied by itself 2 more times (5^2).

All three of these expressions are equal to 5^11 because they all represent the same basic idea: multiplying 5 by itself 11 times. Each of the expressions just breaks down that idea in a slightly different way using the rules of exponents.

Answer 3

Sure! Here are all three expressions together:

1. 5^5 x 5^6
2. 5^10 x 5^1
3. (5^3)^3 x 5^2

All of these expressions are equal to 5^11 because they all describe multiplying 5 by itself 11 times, but they break it down in different ways using the rules of exponents.