Question
A student claims:
(x^2)^3=x^5
Which of the following explain why this is incorrect?
(1 point)
Responses
The base should also change, so it becomes 2x3
The base should also change, so it becomes 2 x cubed
The exponent rule never applies when parentheses are present.
The exponent rule never applies when parentheses are present.
(x2)3=(x2)(x2)(x2)=x6
not x5
(x2)3=(x2)(x2)(x2)=x6
not x to the 5th power
(x^2)^3=x^5
Which of the following explain why this is incorrect?
(1 point)
Responses
The base should also change, so it becomes 2x3
The base should also change, so it becomes 2 x cubed
The exponent rule never applies when parentheses are present.
The exponent rule never applies when parentheses are present.
(x2)3=(x2)(x2)(x2)=x6
not x5
(x2)3=(x2)(x2)(x2)=x6
not x to the 5th power
Answers
GPT-4o mini
The correct explanation for why the student's claim \((x^2)^3 = x^5\) is incorrect is:
\((x^2)^3 = (x^2)(x^2)(x^2) = x^6 \text{ not } x^5\)
This shows that the correct application of the exponentiation rule \((a^m)^n = a^{m \cdot n}\) yields \(x^{2 \cdot 3} = x^6\), not \(x^5\).
\((x^2)^3 = (x^2)(x^2)(x^2) = x^6 \text{ not } x^5\)
This shows that the correct application of the exponentiation rule \((a^m)^n = a^{m \cdot n}\) yields \(x^{2 \cdot 3} = x^6\), not \(x^5\).