Which is equal to $\frac{1}{28^9}$ ? $\newline$ Choices: $\newline$ (A) $-\frac{1}{28^{-9}}$ $\newline$ (B) $\frac{1}{28^{-9}}$ $\newline$ (C) $28^{-9}$ $\newline$ (D) $(-28)^{-9}$

Full solution

Q. Which is equal to

\frac{1}{28^9}

\newline

Choices:

\newline

(A)

-\frac{1}{28^{-9}}

\newline

(B)

\frac{1}{28^{-9}}

\newline

(C)

28^{-9}

\newline

(D)

(-28)^{-9}

Understand given expression: Understand the given expression $\frac{1}{28^9}$ . The given expression is a fraction where $28^9$ is in the denominator. This means we are looking for an expression with a negative exponent that would represent the reciprocal of $28^9$ .
Apply negative exponent rule: Apply the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, to express $\frac{1}{28^9}$ with a negative exponent, we would write it as $28^{-9}$ .
Match with given choices: Match the expression with the given choices. $\newline$ We have determined that $\frac{1}{28^9}$ is equivalent to $28^{-9}$ . Now we need to find this expression among the choices provided. $\newline$ (A) $-\frac{1}{28^{-9}}$ is not correct because it introduces a negative sign in the numerator which is not present in the original expression. $\newline$ (B) $\frac{1}{28^{-9}}$ is not correct because it represents $28^9$ , not $\frac{1}{28^9}$ . $\newline$ (C) $28^{-9}$ is the correct choice because it represents the reciprocal of $28^9$ . $\newline$ (D) $(-28)^{-9}$ is not correct because it introduces a negative sign in the base which is not present in the original expression.