Question
Tyler simplified the expression x Superscript negative 3 Baseline y Superscript negative 9. His procedure is shown below.
x Superscript negative 3 Baseline y Superscript negative 9 = StartFraction 1 Over x cubed EndFraction times StartFraction 1 Over y Superscript negative 9 EndFraction = StartFraction 1 Over x cubed y Superscript negative 9 EndFraction
What is Tyler’s error?
Both powers should be in the numerator with positive exponents.
Both powers should be in the denominator with positive exponents.
The power x cubed should be in the numerator and the power y Superscript 9 in the denominator.
The power y Superscript 9 should be in the numerator and the power x cubed in the denominator.
x Superscript negative 3 Baseline y Superscript negative 9 = StartFraction 1 Over x cubed EndFraction times StartFraction 1 Over y Superscript negative 9 EndFraction = StartFraction 1 Over x cubed y Superscript negative 9 EndFraction
What is Tyler’s error?
Both powers should be in the numerator with positive exponents.
Both powers should be in the denominator with positive exponents.
The power x cubed should be in the numerator and the power y Superscript 9 in the denominator.
The power y Superscript 9 should be in the numerator and the power x cubed in the denominator.
Answers
GPT-4o mini
Tyler's mistake is in how he treated the negative exponent for \( y^{-9} \). When he simplified the expression \( x^{-3} y^{-9} \), he correctly changed \( x^{-3} \) to \( \frac{1}{x^3} \), but he incorrectly managed \( y^{-9} \).
The correct way to handle \( y^{-9} \) is to rewrite it as \( \frac{1}{y^9} \), not \( y^{-9} \) in the denominator. Thus, the final expression should be:
\[
x^{-3} y^{-9} = \frac{1}{x^3} \cdot \frac{1}{y^9} = \frac{1}{x^3 y^9}
\]
Therefore, the correct conclusion is that **both powers should be in the denominator with positive exponents.**
The correct way to handle \( y^{-9} \) is to rewrite it as \( \frac{1}{y^9} \), not \( y^{-9} \) in the denominator. Thus, the final expression should be:
\[
x^{-3} y^{-9} = \frac{1}{x^3} \cdot \frac{1}{y^9} = \frac{1}{x^3 y^9}
\]
Therefore, the correct conclusion is that **both powers should be in the denominator with positive exponents.**