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Select all the expressions that are equivalent to $\frac{6^4}{3^4}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{2^4}$ $\newline$ (B) $2$ $\newline$ (C) $2^4$ $\newline$ (D) $\frac{1}{2^{-4}}$

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Find derivatives using the product rule II

Full solution

Q. Select all the expressions that are equivalent to

\frac{6^4}{3^4}

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{2^4}

\newline

(B)

2

\newline

(C)

2^4

\newline

(D)

\frac{1}{2^{-4}}

Simplify Expression: Simplify the given expression $\frac{6^4}{3^4}$ by recognizing that $\frac{6}{3} = 2$ . Thus, $\frac{6^4}{3^4} = (2)^4$ .
Calculate Result: Calculate $2^4$ to find that $2^4 = 16$ . So, $\frac{6^4}{3^4} = 16$ .
Compare with Choices: Compare the result with the given choices: $\newline$ - (A) $\frac{1}{2^4} = \frac{1}{16}$ which is not equal to $16$ . $\newline$ - (B) $2$ is clearly not equal to $16$ . $\newline$ - (C) $2^4 = 16$ , which matches our result. $\newline$ - (D) $\frac{1}{2^{-4}} = 2^4 = 16$ , which also matches our result.

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