Hint: In ancient times, algebra was used to find linear and quadratic equations. In the 15th century, Ibn al-Banna had introduced the symbol for algebra and mathematics in general. So, it must be after the 15th century that algebraic powers and operations were developed.
Complete step-by-step answer:
The word Algebra literally means the reunion of broken parts. The history of algebra began in ancient Egypt. The word algebra is derived from the language Arabic.
Francois Viete’s work on new algebra at the close of the 16th century was an important step towards modern algebra.
In 1637, Rene Descartes published La Geometrie, inventing analytic geometry and introducing modern algebraic notation.
Another key event in the further development of algebra was the general algebraic solution of the cubic and quartic equations, developed in the mid-16th century.
The idea of a determinant was developed by Japanese mathematician Seki Kowa in the 17th century, followed independently by Gottfried Leibniz ten years later, for the purpose of solving systems of simultaneous linear equations using matrices.
Gabriel Cramer also did some work on matrices and determinants in the 18th century.
Brahmagupta applied algebra to astronomy.
An important development in algebra in the 16th century was the introduction to unknown symbols.
Egyptians used the symbol heap for the unknown in algebra.
And hence in the 16th century algebraic powers and operations were developed. Hence option (a) is the right answer.
Note: For solving this type of questions we need to read the introduction part of the chapters in mathematics. We need to be aware of the basic facts and timelines in the development of content related to mathematics.