Multiply Powers: Calculate 11⁶ × 10⁶ × 12⁶ Step by Step

Question

Insert the corresponding expression:

116×106×126= 11^6\times10^6\times12^6=

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 The entire multiplication operation can be written with exponent (N)
00:13 We will apply this formula
00:18 In multiplication, the order of factors doesn't matter, therefore the expressions are equal
00:24 We will apply this formula to our exercise, and change the order of factors
00:41 This is the solution

Step-by-Step Solution

To address this problem, let's use the power of a product rule:

  • Step 1: We start with 116×106×12611^6 \times 10^6 \times 12^6.
  • Step 2: By the power of a product rule, we can combine these into a single expression: (11×10×12)6(11 \times 10 \times 12)^6.

This equation satisfies the choices given, as all representations like (11×10×12)6(11 \times 10 \times 12)^6, (10×11×12)6(10 \times 11 \times 12)^6, and (12×10×11)6(12 \times 10 \times 11)^6 are equivalent due to the commutative property of multiplication.

Thus, all answers provided are correct, leading us to the choice that recognizes this equivalence:

All answers are correct.

Answer

All answers are correct