Solve Product of Powers: 9¹¹ × 7¹¹ × 6¹¹ Expression

Question

Insert the corresponding expression:

911×711×611= 9^{11}\times7^{11}\times6^{11}=

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)
00:11 We can write the exponent (N) over the entire product
00:15 We can apply this formula to our exercise
00:24 In multiplication, the order of factors doesn't matter, therefore the expressions are equal
00:34 We will apply this formula to our exercise and change the order of factors
00:51 This is the solution

Step-by-Step Solution

To solve the problem 911×711×611= 9^{11} \times 7^{11} \times 6^{11} = , we will apply the Power of a Product rule.

Step 1: Identify the expression and common exponent
The expression given is 911×711×611 9^{11} \times 7^{11} \times 6^{11} . Notice that all three terms share the common exponent 11.

Step 2: Apply the Power of a Product rule
According to the Power of a Product rule, where you have multiple terms each raised to the same power, you can rewrite the expression as a single product raised to that common power. This means:

(9×7×6)11 (9 \times 7 \times 6)^{11}

This expression consolidates the original terms under a single exponent.

Step 3: Verify the form of the solution
The choices provided show the expression in a generalized form without calculating the product. Hence, the expression can be represented as:

(9×7×6)11 (9 \times 7 \times 6)^{11} or (6×7×9)11 (6 \times 7 \times 9)^{11} or (7×6×9)11 (7 \times 6 \times 9)^{11}

Conclusion:
Therefore, any of the options where the bases are multiplied together under the common exponent 11 correctly represent the simplified expression. Thus, the answer is "All answers are correct."

Answer

All answers are correct