Algebra Practice Test

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Which expression correctly represents the multiplication of a^2 and its reciprocal a^-2?

The correct answer is: 1

To determine the product of $a^2$ and its reciprocal $a^{-2}$, we first need to identify the reciprocal of $a^2$. The reciprocal of $a^2$ is $1/a^2$, which can also be expressed as $a^{-2}$. When multiplying $a^2$ by its reciprocal $a^{-2}$, we can use the laws of exponents. Specifically, when we multiply two expressions with the same base, we add their exponents. Therefore: \[ a^2 \cdot a^{-2} = a^{2 + (-2)} = a^{0}. \] According to the properties of exponents, any base raised to the power of 0 equals 1, as long as the base is not zero. Thus, $a^0 = 1$. Therefore, the expression that correctly represents the multiplication of $a^2$ and its reciprocal $a^{-2}$ is indeed equal to 1.