Reduce the Expression: 2⁷ × 3⁷ × 10⁷ Power Product

Question

Reduce the following equation:

27×37×107= 2^7\times3^7\times10^7=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 When we are presented with a multiplication operation where all the factors have the same exponent (N)
00:07 We can write the exponent (N) over the entire multiplication
00:13 We can apply this formula to our exercise
00:21 Now we solve each multiplication separately
00:29 This is the solution

Step-by-Step Solution

To simplify the expression 27×37×107 2^7 \times 3^7 \times 10^7 , we can follow these steps:

  • Step 1: Apply the power of a product rule to combine 27×37 2^7 \times 3^7 into (2×3)7 (2 \times 3)^7 .

  • Step 2: Recognize that 2×3=6 2 \times 3 = 6 , so the expression becomes 67×107 6^7 \times 10^7 .

  • Step 3: Again, apply the power of a product rule to combine 67×107 6^7 \times 10^7 into (6×10)7 (6 \times 10)^7 .

  • Step 4: Calculate 6×10=60 6 \times 10 = 60 , resulting in 607 60^7 .

Therefore, the simplified form of the expression is 607 60^7 . Additionally, since all the provided answer choices (607 60^7 , 67×107 6^7 \times 10^7 , and 27×(3×10)7 2^7 \times (3 \times 10)^7 ) represent equivalent forms of the original expression, all answers are correct.

Conclusion: All answers are correct \boxed{\text{All answers are correct}} .

Answer

All answers are correct