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Select all the expressions that are equivalent to $\frac{6^6}{2^6}$ . $\newline$ Multi-select Choices: $\newline$ (A) $3$ $\newline$ (B) $\frac{1}{3^6}$ $\newline$ (C) $3^0$ $\newline$ (D) $3^6$

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Simplify rational expressions

Full solution

Q. Select all the expressions that are equivalent to

\frac{6^6}{2^6}

.

\newline

Multi-select Choices:

\newline

(A)

3

\newline

(B)

\frac{1}{3^6}

\newline

(C)

3^0

\newline

(D)

3^6

Recognize Simplify Property: First, simplify $\frac{6^6}{2^6}$ by recognizing that $6 = 2 \times 3$ , so $6^6 = (2 \times 3)^6$ . $\newline$ Using the property of exponents, $(ab)^n = a^n \times b^n$ , we get $(2 \times 3)^6 = 2^6 \times 3^6$ . $\newline$ Thus, $\frac{6^6}{2^6} = \frac{2^6 \times 3^6}{2^6}$ .
Cancel Out Terms: Next, cancel out $2^6$ from the numerator and the denominator, which leaves $3^6$ .
Compare with Choices: Now, compare $3^6$ with the given choices: $\newline$ (A) $3$ is $3^1$ , not $3^6$ . $\newline$ (B) $\frac{1}{3^6}$ is the reciprocal of $3^6$ , not equal. $\newline$ (C) $3^0 = 1$ , not $3^6$ . $\newline$ (D) $3^6$ matches exactly.

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