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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))

Which expressions are equivalent to \newline7777777^7\cdot7^7\cdot7^7?\newlineChoose 22 answers:\newline(A) 7872\frac{7^8}{7^2}\newline(B) 76717^6\cdot7^1\newline(C) (72)3(7^2)^3\newline(D)71272\frac{7^{12}}{7^2}

Full solution

Q. Which expressions are equivalent to \newline7777777^7\cdot7^7\cdot7^7?\newlineChoose 22 answers:\newline(A) 7872\frac{7^8}{7^2}\newline(B) 76717^6\cdot7^1\newline(C) (72)3(7^2)^3\newline(D)71272\frac{7^{12}}{7^2}
  1. Understand the original expression: Understand the original expression.\newlineThe original expression is 7777777*7*7*7*7*7, which is 77 raised to the power of 66, or 767^6.
  2. Evaluate option A: Evaluate option A.\newlineOption A is (78)/(72)(7^8)/(7^2). Using the rule of exponents for division, we subtract the exponents: 82=68 - 2 = 6. So, (78)/(72)(7^8)/(7^2) simplifies to 7(82)=767^{(8-2)} = 7^6.
  3. Evaluate option B: Evaluate option B.\newlineOption B is 76×717^6\times7^1. Using the rule of exponents for multiplication, we add the exponents: 6+1=76 + 1 = 7. So, 76×717^6\times7^1 simplifies to 76+1=777^{6+1} = 7^7, which is not equivalent to 767^6.
  4. Evaluate option C: Evaluate option C.\newlineOption C is (72)3(7^2)^3. Using the rule of exponents for powers, we multiply the exponents: 2×3=62 \times 3 = 6. So, (72)3(7^2)^3 simplifies to 72×3=767^{2\times3} = 7^6.
  5. Evaluate option D: Evaluate option D.\newlineOption D is (712)/(72)(7^{12})/(7^2). Using the rule of exponents for division, we subtract the exponents: 122=1012 - 2 = 10. So, (712)/(72)(7^{12})/(7^2) simplifies to 7(122)=7107^{(12-2)} = 7^{10}, which is not equivalent to 767^6.
  6. Select the correct options: Select the correct options.\newlineFrom the evaluations, we see that options A and C are equivalent to 767^6. Therefore, the correct answers are A and C.

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