Which expression is equivalent to (2^9)^8? Choices: (A)1/2^72 (B)1/2^17 (C)2^72 (D)2^17

Simplify Power Rule: Simplify the expression using the power of a power rule, which states (a^m)^n = a^(m*n). Calculation: (2^9)^8 = 2^(9*8) = 2^72 Calculate Exponent: Compare the simplified expression 2^72 with the given choices. (A) 1/2^72 is the reciprocal of 2^72, not equivalent. (B) 1/2^17 is the reciprocal of 2^17, not equivalent. (C) 2^72 matches exactly. (D) 2^17 is not equivalent as it represents a different power of 2.

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Which expression is equivalent to $(2^9)^8$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{2^{72}}$ $\newline$ (B) $\frac{1}{2^{17}}$ $\newline$ (C) $2^{72}$ $\newline$ (D) $2^{17}$

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

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Q. Which expression is equivalent to

(2^9)^8

\newline

Choices:

\newline

(A)

\frac{1}{2^{72}}

\newline

(B)

\frac{1}{2^{17}}

\newline

(C)

2^{72}

\newline

(D)

2^{17}

Simplify Power Rule: Simplify the expression using the power of a power rule, which states $(a^m)^n = a^{m*n}$ . $\newline$ Calculation: $(2^9)^8 = 2^{9*8} = 2^{72}$
Calculate Exponent: Compare the simplified expression $2^{72}$ with the given choices. $\newline$ (A) $\frac{1}{2^{72}}$ is the reciprocal of $2^{72}$ , not equivalent. $\newline$ (B) $\frac{1}{2^{17}}$ is the reciprocal of $2^{17}$ , not equivalent. $\newline$ (C) $2^{72}$ matches exactly. $\newline$ (D) $2^{17}$ is not equivalent as it represents a different power of $2$ .