Which expressions are equivalent to 7*7*7*7*7*7 ? Choose 2 answers: A (7^(8))/(7^(2)) (B) 7^(6)*7^(1) c (7^(2))^(3) D (7^(12))/(7^(2))

Question

Which expressions are equivalent to  7*7*7*7*7*7 ? Choose 2 answers: A  (7^(8))/(7^(2)) (B)  7^(6)*7^(1) c  (7^(2))^(3) D  (7^(12))/(7^(2))

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

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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