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Which expression is equivalent to $(5^9)^4$ ? $\newline$ Choices: $\newline$ (A) $5^{13}$ $\newline$ (B) $\frac{1}{5^{13}}$ $\newline$ (C) $\frac{1}{5^{36}}$ $\newline$ (D) $5^{36}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

(5^9)^4

?

\newline

Choices:

\newline

(A)

5^{13}

\newline

(B)

\frac{1}{5^{13}}

\newline

(C)

\frac{1}{5^{36}}

\newline

(D)

5^{36}

Understand Problem: Understand the problem and apply the power of a power rule. $\newline$ The problem asks us to simplify the expression $(5^9)^4$ . According to the power of a power rule, when we raise a power to another power, we multiply the exponents. $\newline$ Calculation: $(5^9)^4 = 5^{9\times4} = 5^{36}$
Apply Power Rule: Match the simplified expression with the given choices. $\newline$ We have simplified the expression to $5^{36}$ . Now we need to see which of the given choices matches this expression. $\newline$ Choices: $\newline$ (A) $5^{13}$ $\newline$ (B) $\frac{1}{5^{13}}$ $\newline$ (C) $\frac{1}{5^{36}}$ $\newline$ (D) $5^{36}$ $\newline$ The correct choice is (D) $5^{36}$ .

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