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Which expression is equivalent to $(3^4)^5$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{3^9}$ $\newline$ (B) $3^9$ $\newline$ (C) $3^{20}$ $\newline$ (D) $\frac{1}{3^{20}}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

(3^4)^5

?

\newline

Choices:

\newline

(A)

\frac{1}{3^9}

\newline

(B)

3^9

\newline

(C)

3^{20}

\newline

(D)

\frac{1}{3^{20}}

Understand Problem: Understand the problem and apply the power of a power rule. $\newline$ The problem asks us to simplify the expression $(3^4)^5$ . According to the power of a power rule, when we raise a power to another power, we multiply the exponents. $\newline$ Calculation: $(3^4)^5 = 3^{(4*5)} = 3^{20}$
Apply Power Rule: Match the simplified expression with the given choices. $\newline$ We have simplified the expression to $3^{20}$ . Now we need to see which of the given choices matches this expression. $\newline$ Choices: $\newline$ (A) $\frac{1}{3^9}$ $\newline$ (B) $3^9$ $\newline$ (C) $3^{20}$ $\newline$ (D) $\frac{1}{3^{20}}$ $\newline$ The correct match is choice (C) $3^{20}$ .

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