Sam, Max, and Edith completed the problems below.
Sam: 7^3∙7^5=7^8
Max: 7^3∙7^5=7^15
Edith: 7^3∙7^5=49^8
Who completed the problem correctly?
What did the other two students do wrong in their answers?
Edith completed the problem correctly.
In Sam's answer, he added the exponents instead of multiplying them. The correct answer should be 7^8, not 7^8+3.
In Max's answer, he added the exponents instead of multiplying them. The correct answer should be 7^15, not 7^3+5.
To determine who completed the problem correctly, let's evaluate each student's answer step by step.
Sam's answer: 7^3 ∙ 7^5 = 7^8
To multiply powers with the same base, we add the exponents. So, 7^3 ∙ 7^5 = 7^(3+5) = 7^8.
Therefore, Sam's answer is correct.
Max's answer: 7^3 ∙ 7^5 = 7^15
Max made an error while adding the exponents. Instead of adding 3 and 5, he calculated 3 + 5 as 15. Therefore, Max's answer is incorrect.
Edith's answer: 7^3 ∙ 7^5 = 49^8
Edith cubed the base 7 to get 49, and then raised it to the power of 8. However, this is not a correct solution. The proper computation would be to multiply the exponents, not raise the base to the power of the exponent. Therefore, Edith's answer is incorrect.
In conclusion, Sam completed the problem correctly, while Max and Edith made mistakes in their answers by either adding the exponents incorrectly or raising the base to the power of the exponent instead of multiplying the exponents.