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Which expression is equivalent to $10^6 \times 7^6$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{70^6}$ $\newline$ (B) $70^6$ $\newline$ (C) $70^{12}$ $\newline$ (D) $70^{36}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

10^6 \times 7^6

?

\newline

Choices:

\newline

(A)

\frac{1}{70^6}

\newline

(B)

70^6

\newline

(C)

70^{12}

\newline

(D)

70^{36}

Identify Bases and Exponents: Identify the bases and exponents in the expression $10^6$ and $7^6$ . $\newline$ Calculation: $10^6$ means $10$ raised to the power of $6$ ; $7^6$ means $7$ raised to the power of $6$ .
Combine Using Exponent Property: Combine the expressions using the property of exponents for multiplication $a^m * b^m = (a*b)^m$ . Calculation: $10^6 * 7^6 = (10*7)^6 = 70^6$ .
Match with Choices: Match the result with the given choices. $\newline$ Calculation: The expression $70^6$ corresponds to choice $(B)$ .

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