23.) Emma, Erin, and Eden completed the problem to the right.
Emma 6^2 X 6^5=36^7
Erin 6^2 X 6^5=6^10
Eden 6^2 X 6^5=6^7
a. who completed the problem correctly?
b. what did the other two students do wrong in their answers?
a. Eden completed the problem correctly.
b. Emma made the mistake of multiplying the exponents instead of adding them, and Erin made the mistake of adding the exponents instead of multiplying them.
how do u know
To check:
- Emma's answer is 6^2 x 6^5 = 6^(2+5) = 6^7, not 36^7.
- Erin's answer is 6^2 x 6^5 = 6^(2x5) = 6^10, not 6^7.
- Eden's answer is 6^2 x 6^5 = 6^(2+5) = 6^7, which is correct.
Therefore, Eden completed the problem correctly, while Emma and Erin made mistakes.
but what if emma had 36^7 and erin had 6^10 and eden had 6^7? what would i put then
If Emma had 36^7 and Erin had 6^10, then both Emma and Erin completed the problem incorrectly. Only Eden's answer of 6^2 x 6^5 = 6^7 would be correct.
You are correct. I apologize for the confusion in my previous response. If Emma's answer was 36^7 and Erin's answer was 6^10, then only Eden's answer of 6^2 x 6^5 = 6^7 would be correct. Emma and Erin both made errors in their calculations.
explain how
Certainly.
- Emma's answer of 36^7 implies that she converted the bases to 36, using the property that a^b x a^c = a^(b+c). However, the problem only involves the base 6. Therefore, Emma's answer is incorrect.
- Erin's answer of 6^10 implies that she added the exponents 2 and 5 together instead of multiplying them, using the same property as Emma. This mistake also leads to an incorrect answer.
Eden's answer of 6^2 x 6^5 = 6^(2+5) = 6^7 is the correct application of the property where when we multiply two exponential expressions with the same base, we can add their exponents.
explain how emma got hers wrong again im dumb
Sure, I'll explain.
Emma's equation was 6^2 x 6^5 which can be simplified using the property that when two exponential expressions that have the same base are multiplied together, we can add their exponents.
So, 6^2 x 6^5 can be written as 6^(2+5) = 6^7.
However, Emma multiplied the exponents instead of adding them.
So, Emma's answer was 6^2 x 6^5 = 6^(2 x 5) = 6^10, which is not equal to the correct answer 6^7.
no emmas answer was 36^7
I apologize for the mistake. Emma converted the bases to 36 instead of adding 2 and 5 to get 7 as the exponent. Therefore, Emma's answer of 36^7 is also incorrect, as the answer should only involve the base 6.
I apologize for the confusion. Emma's answer 36^7 is not correct as it involves the base 36, which is not relevant to the problem.
The correct answer to the problem 6^2 x 6^5 is 6^(2+5) = 6^7, as I mentioned earlier. Emma made the mistake of converting the bases to 36 and getting the incorrect answer.