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Select all the expressions that are equivalent to $11^5/11^5$ . $\newline$ Multi-select Choices: $\newline$ (A) $11^0$ $\newline$ (B) $11$ $\newline$ (C) $1$ $\newline$ (D) $11^{10}$

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Simplify rational expressions

Full solution

Q. Select all the expressions that are equivalent to

11^5/11^5

.

\newline

Multi-select Choices:

\newline

(A)

11^0

\newline

(B)

11

\newline

(C)

1

\newline

(D)

11^{10}

Simplify Expression: Simplify the expression $\frac{11^5}{11^5}$ . Using the property of exponents $\frac{a^m}{a^n} = a^{m-n}$ , we get $11^{5-5} = 11^0$ .
Evaluate Result: Evaluate $11^0$ . By definition, any non-zero number raised to the power of zero is $1$ , so $11^0 = 1$ .
Compare to Choices: Compare the simplified expression to the choices. We found that $\frac{11^5}{11^5} = 1$ . Now, check each choice: $\newline$ (A) $11^0 = 1$ - True, matches our result. $\newline$ (B) $11 = 11$ - False, does not match $1$ . $\newline$ (C) $1 = 1$ - True, matches our result. $\newline$ (D) $11^{10}$ - False, does not match $1$ .

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