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Which expression is equivalent to $(11^4)^2$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{11^6}$ $\newline$ (B) $11^6$ $\newline$ (C) $\frac{1}{11^8}$ $\newline$ (D) $11^8$

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Identify equivalent exponential expressions I

Full solution

Q. Which expression is equivalent to

(11^4)^2

?

\newline

Choices:

\newline

(A)

\frac{1}{11^6}

\newline

(B)

11^6

\newline

(C)

\frac{1}{11^8}

\newline

(D)

11^8

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. $\newline$ When we raise a power to another power, we multiply the exponents. $\newline$ $(a^m)^n = a^{(m*n)}$
Apply Rule to Calculation: Apply the exponent rule to $(11^4)^2$ . We have $(11^4)^2$ , which means we need to multiply the exponents $4$ and $2$ . $(11^4)^2 = 11^{(4*2)} = 11^8$
Choose Equivalent Expression: Choose the equivalent expression for 11^4)^2\. From the calculation in Step \$(2), we have determined that $11^4)^2\ is equivalent to \$(11^8)$ . Therefore, the correct choice is (D) $(11^8)$ .

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