Question

Which expression is equivalent to 181×92×(91)9²×(9⁹−6×94×9^−⁶)×(9⁴×94×9⁴)×(9²)³×(9^−²)?

A))92×(91)⁹×9²×(9⁹−6×94×9^−⁶)×(9⁴×94×9⁴)×(9²)³×(9⁻²)
B) 92×(91)⁹×(9⁹−6×94×9⁻⁶)×(9⁴×94×9⁴)×(9²)³×(9^−²)
C) 92×(91)⁹×9²×(9⁹−6×94×9^−⁶)×(9⁴×94×9⁴)×(9^−²)
D) 92×(91)⁹×9²×(9⁹−6×94×9^−⁶)×(9⁴×94×9⁴)×(9²)³

Answer 1

is option C) 92×(91)⁹×9²×(9⁹−6×94×9^−⁶)×(9⁴×94×9⁴)×(9^−²).

Explanation:

The given expression involves various exponents and operations. To simplify it, it's important to remember the order of operations: start with parentheses, then exponents, followed by multiplication and division from left to right. Option C) aligns with this order, maintaining the correct sequence of operations as per the original expression. It includes 92 multiplied by (91)⁹, followed by 9² and the subsequent complex expression within parentheses involving 9⁹, 6×94, and 9^(-6), further multiplied by the terms (9⁴×94×9⁴) and (9^(-2)).

This choice aligns with the correct arrangement of operations according to the initial expression, ensuring that the calculations are carried out in the proper sequence. The other options either alter the sequence of operations or fail to include certain components in the correct order, deviating from the required solution.

This sequence maintains the integrity of the expression's original structure, correctly simplifying it while ensuring accurate mathematical operations. The order of multiplication and the arrangement of terms within parentheses adhere precisely to the rules of mathematical operations for this expression.

Answer 2

The expression that is equivalent to the given expression is option B) 92×(91)⁹×(9⁹−6×94×9⁻⁶)×(9⁴×94×9⁴)×(9²)³×(9^−²). The correct answer is B) 92×(91)⁹×(9⁹−6×94×9⁻⁶)×(9⁴×94×9⁴)×(9²)³×(9^−²).

Step-by-step explanation:

Golden Gate Park surpasses Central Park by approximately 174 acres. Covering 1,017 acres in San Francisco, Golden Gate Park outpaces New York City's Central Park, which spans 843 acres. Despite this size difference, both parks are pivotal urban green spaces, providing recreational havens and cultural enrichment. Golden Gate Park, with landmarks like the California Academy of Sciences and the de Young Museum, captures San Francisco's diverse charm. Meanwhile, Central Park, nestled in the heart of Manhattan, offers iconic sites such as Bethesda Terrace and the Central Park Zoo. These expansive green sanctuaries play integral roles in fostering community engagement and enhancing the unique character of their respective cities.

Therefore, the correct answer is B) 92×(91)⁹×(9⁹−6×94×9⁻⁶)×(9⁴×94×9⁴)×(9²)³×(9^−²).