Final answer:
Anja incorrectly simplified the original expression by combining constants and exponents incorrectly. The correct simplification should result in -2/x5 by dividing 10 by -5 and subtracting the exponents 10 - (-5) to get x5.
Step-by-step explanation:
It appears that Anja made a mistake in simplifying the expression startfraction 10 x-5 over -5 x10 endfraction. The rule of negative exponents states that a term with a negative exponent is flipped to the other side of the fraction (numerator to denominator or vice versa) and its exponent becomes positive. Thus, x-5 actually becomes 1/x5 when moved from the numerator to the denominator.
Applying this rule and simplifying the initial expression, we first divide 10 by -5, yielding -2. Then, we apply the exponent properties: x-5 multiplied by x10 is the same as x10-5 which simplifies to x5. Therefore, the correct simplified form of Anja's expression is startfraction -2 over x5 endfraction, not startfraction 15 over x15 endfraction as she incorrectly concluded.