Q. Which expressions are equivalent to 77⋅77⋅77?Choose 2 answers:(A) 7278(B) 76⋅71(C) (72)3(D)72712
Understand the original expression: Understand the original expression.The original expression is 7∗7∗7∗7∗7∗7, which is 7 raised to the power of 6, or 76.
Evaluate option A: Evaluate option A.Option A is (78)/(72). Using the rule of exponents for division, we subtract the exponents: 8−2=6. So, (78)/(72) simplifies to 7(8−2)=76.
Evaluate option B: Evaluate option B.Option B is 76×71. Using the rule of exponents for multiplication, we add the exponents: 6+1=7. So, 76×71 simplifies to 76+1=77, which is not equivalent to 76.
Evaluate option C: Evaluate option C.Option C is (72)3. Using the rule of exponents for powers, we multiply the exponents: 2×3=6. So, (72)3 simplifies to 72×3=76.
Evaluate option D: Evaluate option D.Option D is (712)/(72). Using the rule of exponents for division, we subtract the exponents: 12−2=10. So, (712)/(72) simplifies to 7(12−2)=710, which is not equivalent to 76.
Select the correct options: Select the correct options.From the evaluations, we see that options A and C are equivalent to 76. Therefore, the correct answers are A and C.
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