Which expressions are equivalent to $7^7\cdot7^7\cdot7^7\cdot7^7\cdot7^7\cdot7^7?$ $\newline$ Choose $2$ answers: $\newline$ (A) $\frac{7^8}{7^2}$ $\newline$ (B) $7^6\cdot7^1$ $\newline$ (C) $\left(7^2\right)^3$ $\newline$ (D) $\frac{7^{12}}{7^2}$

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Math Problems

Grade 8

Divide numbers written in scientific notation

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Q. Which expressions are equivalent to

7^7\cdot7^7\cdot7^7\cdot7^7\cdot7^7\cdot7^7?

\newline

Choose

2

answers:

\newline

(A)

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

\newline

(B)

7^6\cdot7^1

\newline

(C)

\left(7^2\right)^3

\newline

(D)

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

Understand original expression: Understand the original expression. $\newline$ The original expression is $7*7*7*7*7*7$ , which is $7$ multiplied by itself $6$ times. $\newline$ This can be written in exponential form as $7^6$ .
Analyze option A: Analyze option A. $\newline$ Option A is $(7^8)/(7^2)$ . To determine if this is equivalent to $7^6$ , we can use the rule of exponents for division, which states that $a^{m}/a^{n} = a^{(m-n)}$ . $\newline$ So, $(7^8)/(7^2) = 7^{(8-2)} = 7^6$ . $\newline$ This shows that option A is equivalent to the original expression.
Analyze option B: Analyze option B. $\newline$ Option B is $7^6\times7^1$ . To determine if this is equivalent to $7^6$ , we can use the rule of exponents for multiplication, which states that $a^{m}\times a^{n} = a^{m+n}$ . $\newline$ So, $7^6\times7^1 = 7^{6+1} = 7^7$ . $\newline$ This shows that option B is not equivalent to the original expression.
Analyze option C: Analyze option C. $\newline$ Option C is $(7^2)^3$ . To determine if this is equivalent to $7^6$ , we can use the rule of exponents for powers, which states that $(a^m)^n = a^{m*n}$ . $\newline$ So, $(7^2)^3 = 7^{2*3} = 7^6$ . $\newline$ This shows that option C is equivalent to the original expression.
Analyze option D: Analyze option D. $\newline$ Option D is $(7^{12})/(7^{2})$ . To determine if this is equivalent to $7^{6}$ , we can use the rule of exponents for division. $\newline$ So, $(7^{12})/(7^{2}) = 7^{(12-2)} = 7^{10}$ . $\newline$ This shows that option D is not equivalent to the original expression.