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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) $2^0$ $\newline$ (C) $2$ $\newline$ (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)

2^0

\newline

(C)

2

\newline

(D)

\frac{1}{2^4}

Simplify Fraction: First, simplify $\frac{6^4}{3^4}$ by recognizing that $\frac{6}{3} = 2$ , so $\frac{6^4}{3^4} = (2)^4$ . $\newline$ Calculation: $2^4 = 16$ .
Evaluate Choices: Next, evaluate each choice to see if it equals $16$ . $\newline$ (A) $\frac{1}{2^{-4}}$ simplifies to $2^4$ because $\frac{1}{a^{-b}} = a^b$ . $\newline$ Calculation: $2^4 = 16$ .
Choice (A): (B) $2^0$ simplifies to $1$ . $\newline$ Calculation: $2^0 = 1$ .
Choice (B): (C) The value of $2$ is just $2$ , not raised to any power. $\newline$ Calculation: $2 = 2$ .
Choice (C): (D) $\frac{1}{2^4}$ simplifies to $\frac{1}{16}$ . $\newline$ Calculation: $\frac{1}{16} = 0.0625$ .

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