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.

Answer 1

Both powers should be in the denominator with positive exponents.

Reason: x^{-3} y^{-9} = (1/x^3)(1/y^9) = 1/(x^3 y^9). Tyler incorrectly replaced y^{-9} by 1/(y^{-9}) instead of 1/y^9.