Question

Select all the equivalent expressions to a² / a⁹ Assume a doesn't equal 0.

a) a² / a⁹
b) a⁷
c) a⁻⁷
d) a⁻²

Answer 1

The equivalent expression to the algebraic expression a² / a¹ is c) a¯·, derived by subtracting the exponents (a²-¹ = a¹(-7)).

Step-by-step explanation:

The student's question pertains to simplifying the algebraic expression a² / a¹ under the assumption that a does not equal 0. In the laws of exponents, when you divide powers with the same base, you subtract the exponents. Therefore:

a² / a¹ = a²-¹ = a²-(9) = a¹(-7)a· is not equivalent because it implies multiplication of exponents, not division.a¯· is equivalent because it correctly represents a²-¹.a¯² is not equivalent because it suggests that the exponent on a is -2, which is not the result of a²-¹.

Hence, the equivalent expression to a² / a¹ is c) a¯·