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Which expression is equivalent to $(10^6)^4$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{10^{24}}$ $\newline$ (B) $10^{24}$ $\newline$ (C) $\frac{1}{10^{10}}$ $\newline$ (D) $10^{10}$

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Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

(10^6)^4

?

\newline

Choices:

\newline

(A)

\frac{1}{10^{24}}

\newline

(B)

10^{24}

\newline

(C)

\frac{1}{10^{10}}

\newline

(D)

10^{10}

Understand the problem: Understand the problem. $\newline$ We need to find the equivalent expression for the power of a power, $(10^6)^4$ . $\newline$ When we raise a power to a power, we multiply the exponents. $\newline$ $a^{(m^n)} = a^{(m*n)}$
Apply power rule: Apply the power of a power rule. $\newline$ $(10^6)^4 = 10^{6\times4}$ $\newline$ Calculate the product of the exponents. $\newline$ $10^{6\times4} = 10^{24}$
Match with choices: Match the result with the given choices. $\newline$ The calculation from Step $2$ gives us $10^{24}$ , which corresponds to choice (B).

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