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

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

(2^8)^1

?

\newline

Choices:

\newline

(A)

\frac{1}{2^9}

\newline

(B)

\frac{1}{2^8}

\newline

(C)

2^8

\newline

(D)

2^9

Simplify Exponent: Simplify the expression $(2^8)^1$ . When an exponent is raised to another exponent, you multiply the exponents. $(2^8)^1 = 2^{(8*1)} = 2^8$
Compare Choices: Compare the simplified expression to the given choices. $\newline$ The simplified expression is $2^8$ . Now we need to see which choice matches this expression. $\newline$ (A) $\frac{1}{2^9}$ is not equal to $2^8$ . $\newline$ (B) $\frac{1}{2^8}$ is not equal to $2^8$ . $\newline$ (C) $2^8$ is exactly the same as our simplified expression. $\newline$ (D) $2^9$ is not equal to $2^8$ .
Select Correct Choice: Select the correct choice. $\newline$ Since $2^8$ matches choice (C), the equivalent expression to $(2^8)^1$ is $2^8$ .

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