Final answer:
None of the simplifications given are correct. The correct approach for simplifying (9²) * 9 is to use the power of a power rule, yielding 9³ or 729, not 9. Remember to apply correct exponent rules when dealing with exponentials.
Step-by-step explanation:
None of the provided simplifications accurately explain the given mathematical statement. In the case of (9²) * 9, which is read as nine squared times nine, the correct simplification is to apply the power of a power rule, where you multiply the exponents. Since 9² equals 81, multiplying by another 9 gives us 9³, which is 729, not 9. The statement 9 + (9 * 9) = 9 * 9 is illogical because addition cannot simplify to multiplication without other operations or factors. Consequently, the expression 9.1=9 is incorrect because 9.1 is a decimal number and not equal to the integer 9.
When simplifying exponentials, such as in cubing or raising to a power, it's important to remember the correct mathematical rules: x² * x = x³ and (x³)² equals x¹, which is the base number multiplied by itself three times twice, resulting in the exponents being multiplied.