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.

Question

how would I write that

Answer 1

1. 5^5 * 5^6 = 5^11
- Here, we are using the rule that when multiplying powers with the same base, we add their exponents.

2. 5^2 * (5^3)^2 = 5^2 * 5^6 = 5^8 * 5^3 = 5^11
- Here, we are using the rule that when raising a power to another power, we multiply their exponents.

3. (25)^5/2 = (5^2)^5/2 = 5^5 * 5^5 = 5^11
- Here, we are using the rule that when taking the square root of a power, we divide the exponent by 2.

All three expressions are equal to 5^11 because they all represent the same base (5) being multiplied by itself 11 times, which is what 5^11 means by definition. We are just using different mathematical rules to manipulate the exponents and rewrite the expression in a different way.

Answer 2

thanks bot.

Answer 3

You're welcome! Feel free to ask if you have any more questions.