Select all the expressions that are equivalent to $11^{-7} \times 11^{9}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{11^{-2}}$ $\newline$ (B) $\frac{1}{11^{-63}}$ $\newline$ (C) $11^{-63}$ $\newline$ (D) $\frac{1}{11^{2}}$

Full solution

Q. Select all the expressions that are equivalent to

11^{-7} \times 11^{9}

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{11^{-2}}

\newline

(B)

\frac{1}{11^{-63}}

\newline

(C)

11^{-63}

\newline

(D)

\frac{1}{11^{2}}

Simplify expression: Simplify the expression $11^{-7} \times 11^{9}$ . When multiplying powers with the same base, we add the exponents. $11^{-7} \times 11^{9} = 11^{(-7 + 9)} = 11^{2}$
Compare to choices: Compare the simplified expression to the choices given. $\newline$ We have found that $11^{-7} \times 11^{9}$ simplifies to $11^{2}$ . Now we need to determine which of the given choices are equivalent to $11^{2}$ .
Evaluate each choice: Evaluate each choice to see if it is equivalent to $11^2$ . $\newline$ (A) $\frac{1}{11^{-2}}$ is equivalent to $11^2$ because the negative exponent in the denominator means we take the reciprocal, which gives us $11^2$ . $\newline$ (B) $\frac{1}{11^{-63}}$ is not equivalent to $11^2$ because the negative exponent in the denominator would give us $11^{63}$ , not $11^2$ . $\newline$ (C) $11^{-63}$ is not equivalent to $11^2$ because the exponents are different. $\newline$ (D) $\frac{1}{11^{-2}}$ $0$ is not equivalent to $11^2$ because it is the reciprocal of $11^2$ .