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Which expression is equivalent to $(6^4)^9$ ? $\newline$ Choices: $\newline$ (A) $6^{13}$ $\newline$ (B) $\frac{1}{6^{36}}$ $\newline$ (C) $\frac{1}{6^{13}}$ $\newline$ (D) $6^{36}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

(6^4)^9

?

\newline

Choices:

\newline

(A)

6^{13}

\newline

(B)

\frac{1}{6^{36}}

\newline

(C)

\frac{1}{6^{13}}

\newline

(D)

6^{36}

Understand Exponent Properties: Understand the properties of exponents. When raising a power to a power, you multiply the exponents. $(6^4)^9 = 6^{(4*9)}$
Calculate New Exponent: Calculate the new exponent. Multiply the exponents $4$ and $9$ to find the equivalent single exponent. $6^{(4*9)} = 6^{36}$
Match with Choices: Match the result with the given choices. $\newline$ The calculation from Step $2$ gives us $6^{36}$ , which corresponds to choice (D).

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