Which expressions are equivalent to $\newline$ $7 \times 7 \times 7 \times 7 \times 7 \times 7$ ? $\newline$ Choose $\newline$ $2$ answers: $\newline$ A $\newline$ $\frac{7^{8}}{7^{2}}$ $\newline$ B $\newline$ $7^{6} \times 7^{1}$ $\newline$ C $\newline$ $(7^{2})^{3}$ $\newline$ D $\newline$ $\frac{7^{12}}{7^{2}}$

Full solution

Q. Which expressions are equivalent to

\newline

7 \times 7 \times 7 \times 7 \times 7 \times 7

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Choose

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2

answers:

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\frac{7^{8}}{7^{2}}

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7^{6} \times 7^{1}

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(7^{2})^{3}

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\frac{7^{12}}{7^{2}}

Understand given expression: Understand the given expression. $\newline$ The given expression is $7*7*7*7*7*7$ , which is $7$ raised to the power of $6$ , or $7^6$ .
Analyze option A: Analyze option A. $\newline$ Option A is $(7^8)/(7^2)$ . To determine if this is equivalent to $7^6$ , we apply the rule of exponents for division. $\newline$ $(7^8)/(7^2) = 7^{(8-2)} = 7^6$ .
Analyze option B: Analyze option B. $\newline$ Option B is $7^6\times7^1$ . To determine if this is equivalent to $7^6$ , we apply the rule of exponents for multiplication. $\newline$ $7^6\times7^1 = 7^{6+1} = 7^7$ , which is not equivalent to $7^6$ .
Analyze option C: Analyze option C. $\newline$ Option C is 7^2)^3\. To determine if this is equivalent to \$7^6, we apply the rule of exponents for powers raised to powers. $\newline$ $(7^2)^3 = 7^{(2*3)} = 7^6$ .
Analyze option D: Analyze option D. $\newline$ Option D is $(7^{12})/(7^{2})$ . To determine if this is equivalent to $7^{6}$ , we apply the rule of exponents for division. $\newline$ $(7^{12})/(7^{2}) = 7^{(12-2)} = 7^{10}$ , which is not equivalent to $7^{6}$ .