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.
Plz help it's urgent.
I apologize for the delay in response. Here are three ways to write 5^11 as the product of two powers:
1. 5^7 x 5^4 = 78125 x 625 = 48828125
2. 5^6 x 5^5 = 15625 x 3125 = 48828125
3. 5^10 x 5^1 = 9765625 x 5 = 48828125
All three expressions are equal to 5^11 because they all represent the same quantity, which is 5 multiplied by itself 11 times. This is because when we multiply two powers with the same base, we add their exponents, as mentioned by the earlier user.
doesn't 5^11=5^a * 5^b where a+b=11?
oh, right...
Ain't no way that this was posted in 2013 and they're still no answer ðŸ˜
Sure! I can help you with that. To write 5^11 as the product of two powers, we need to find different ways to break down the exponent 11.
Method 1:
We can write 11 as the sum of two exponents: 11 = 10 + 1. Therefore, we can rewrite 5^11 as (5^10) * (5^1).
Method 2:
We can write 11 as the sum of two different exponents: 11 = 5 + 6. Thus, we can express 5^11 as (5^5) * (5^6).
Method 3:
Another way to represent 11 as the sum of exponents is: 11 = 3 + 8. This allows us to write 5^11 as (5^3) * (5^8).
Now, let's explain why all three expressions are equal to 5^11:
Using the exponentiation rule, when we multiply two powers with the same base (in this case, both are 5), we add the exponents. Therefore, (5^10) * (5^1) becomes 5^(10+1), which equals 5^11.
Similarly, in the second expression, (5^5) * (5^6) can be written as 5^(5+6), resulting in 5^11.
Finally, in the third expression, (5^3) * (5^8) can be expressed as 5^(3+8), which is again equal to 5^11.
So all three expressions, (5^10) * (5^1), (5^5) * (5^6), and (5^3) * (5^8), represent 5^11 because they follow the same rule of adding the exponents when multiplying powers with the same base.