In solving the given problem, we need to identify the errors Javier made in his calculations. Here’s the step-by-step reasoning:
1. Error Analysis when raising [tex]\( x \)[/tex] to the third power:
- Javier raised [tex]\( x \)[/tex] to the third power.
- He wrote that [tex]\( \left(x^1\right)^3 = x^4 \)[/tex].
- This is incorrect because [tex]\( (x^1)^3 = x^{1 \cdot 3} = x^3 \)[/tex].
- Therefore, the correct statement should be:
"When Javier raised [tex]\( x \)[/tex] to the third power, he wrote that [tex]\( \left(x^1\right)^3 = x^4 \)[/tex], but it equals [tex]\( x^3 \)[/tex]".
2. Error Analysis in the last step involving exponents:
- In the last step, Javier divided the exponents.
- He should have used the quotient of powers property, which states that when dividing like bases, you subtract the exponents: [tex]\( \frac{x^m}{x^n} = x^{m-n} \)[/tex].
- Thus, the correct statement should be:
"In the last step, Javier divided the exponents. He should have used the quotient of powers property and subtracted them."
From the analysis above, the response should include the following two statements:
1. When Javier raised [tex]\( x \)[/tex] to the third power, he wrote that [tex]\( \left(x^1\right)^3 = x^4 \)[/tex], but it equals [tex]\( x^3 \)[/tex].
2. In the last step, Javier divided the exponents. He should have used the quotient of powers property and subtracted them.
Therefore, the final answer is:
- "When Javier raised [tex]\( x \)[/tex] to the third power, he wrote that [tex]\( \left(x^1\right)^3 = x^4 \)[/tex], but it equals [tex]\( x^3 \)[/tex]."
- "In the last step, Javier divided the exponents. He should have used the quotient of powers property and subtracted them."
