The expressions which is equivalent to the given expression; 3^(2x -3) is; the quantity 9 to the power of x end quantity over 27.
Option (A) is correct.
It is required to choose the expressions.
What are the laws of indices ?
Index laws are the rules for simplifying expressions involving powers of the same base number. Index (indices) is the exponent which is raised to a number.
Given:
It follows from the task content that the equivalent expression as in the task content can be determined by the laws of Indices.
Now, according to laws of indices;
[tex]3^{2x} =( 3^{2}) ^{x}[/tex]
Thus, we now have;
[tex]= (3^{2} )^{x} )/3^{3} \\= (9^{x} )/3^{3} \\= (9^{x} )/27[/tex]
Therefore, the expressions which is equivalent to the given expression; 3^(2x -3) is; the quantity 9 to the power of x end quantity over 27.
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