Simplify. Assume that variables in the exponent represent nonzero integers and that all other variables are not 0.
-$\frac { z ^ { 9 x + 2 \cdot z ^ { 3 x } } } { z ^ { x } }$
A) $z ^ { 6 x + 2 }$
B) $z ^ { 8 x }$
C) $z ^ { 11 x + 2 }$
D) $z ^ { 14 x }$

Question

Quizplus · Accepted Answer

To simplify the expression, use the properties of exponents. The given expression is $\frac { z ^ { 9 x + 2 \cdot z ^ { 3 x } } } { z ^ { x } }$. This seems to be a typographical error because the exponent cannot have a variable raised to another variable in this context. Assuming the correct expression is $\frac { z ^ { 9 x + 2 } } { z ^ { x } }$, you subtract the exponents when dividing like bases: $9x + 2 - x = 8x + 2$. However, given the options and the likely intended simplification process, the correct interpretation aligns with option C, suggesting a mistake in the transcription of the problem. The correct simplification, based on the options provided and common rules of exponents, would be to subtract the exponent in the denominator from the exponent in the numerator, which would correctly yield $z^{8x + 2}$ if the problem was transcribed as intended. However, none of the options match this result, indicating a misunderstanding in the problem's presentation. Given the options and assuming a mistake in the interpretation of the problem's original text, the closest correct approach would be to consider the properties of exponents correctly, which might lead to option C being selected based on an arithmetic or transcription error.

Simplify Assume That Variables in the Exponent Represent Nonzero Integers z9x+2⋅z3xzx\frac { z ^ { 9 x + 2 \cdot z ^ { 3 x } } } { z ^ { x } }zxz9x+2⋅z3x​

Simplify Assume That Variables in the Exponent Represent Nonzero Integers $\frac { z ^ { 9 x + 2 \cdot z ^ { 3 x } } } { z ^ { x } }$