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Which expression is equivalent to $(2^6)^6$ ? $\newline$ Choices: $\newline$ (A) $2^{36}$ $\newline$ (B) $2^{12}$ $\newline$ (C) $\frac{1}{2^{36}}$ $\newline$ (D) $\frac{1}{2^{12}}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

(2^6)^6

?

\newline

Choices:

\newline

(A)

2^{36}

\newline

(B)

2^{12}

\newline

(C)

\frac{1}{2^{36}}

\newline

(D)

\frac{1}{2^{12}}

Simplify using power rule: Step $1$ : Simplify the expression using the power of a power rule. $\newline$ $(2^6)^6 = 2^{(6\times6)}$ $\newline$ Calculation: $6\times6 = 36$
Write simplified expression: Step $2$ : Write the simplified expression. $\newline$ $(2^6)^6 = 2^{36}$
Match with choices: Step $3$ : Match the simplified expression with the given choices. $2^{36}$ corresponds to choice (A) $2^{36}$ .

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