Calculate (2×5×6×4)^20: Solving a Complex Power Expression

Question

Insert the corresponding expression:

(2×5×6×4)20= \left(2\times5\times6\times4\right)^{20}=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 Let's solve one multiplication at a time
00:15 This is one solution to the question
00:21 According to the laws of exponents, a multiplication where all terms are raised to power (N)
00:25 equals a multiplication where each factor is raised to the same power (N)
00:28 We'll apply this formula to our exercise
00:35 This is the solution

Step-by-Step Solution

To solve the problem, we need to evaluate the expression (2×5×6×4)20 \left(2 \times 5 \times 6 \times 4\right)^{20} .

Step 1: Calculate the product inside the parenthesis:

2×5×6×4 2 \times 5 \times 6 \times 4 .

Breaking it down, we have:

  • 2×5=10 2 \times 5 = 10 .
  • 6×4=24 6 \times 4 = 24 .
  • Therefore, the product is 10×24 10 \times 24 .

Step 2: Apply the power of a product rule:

(10×24)20 (10 \times 24)^{20} can be rewritten using the power of a product rule:

1020×2420 10^{20} \times 24^{20} .

Step 3: Compare with the given choices:

  • Choice 2: 1020×2420 10^{20} \times 24^{20} matches the calculation directly.
  • Choice 3: 24020 240^{20} matches (10×24)20 (10 \times 24)^{20} if calculated directly without breaking into components.

Therefore, both expressions in options Choice 2 and Choice 3 are equivalent to the given expression (2×5×6×4)20 (2 \times 5 \times 6 \times 4)^{20} .

Thus, the correct choice according to the problem is: B+C are correct.

Answer

B+C are correct