1

Problem

Simplify the expression using the Power of a Product Rule: \$ (3x 3y)^2 \$

2

Step

The given expression

\$ (3x 3y)^2 \$

3

Formula

Apply the Power of a Product Rule, which states that \$ (ab)^n = a^n \times b^n \$.

4

Hint

Apply the rule to the expression: \$ (3x 3y)^2 = 3^2 \times x^2 \times 3^2 \times y^2 \$.

5

Step

Now, we can simplify:

\$ (3x 3y)^2 = 9 \times x^2 \times 9 \times y^2 \$

6

Step

Now, we can simplify further:

\$ (3x 3y)^2 = 81x^2 y^2 \$

7

Solution

Thus, \$ (3x 3y)^2 \$ simplifies to \$ 81(x^2) (y^2) \$.

8

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

9

Choice-A

This choice is incorrect, the correct coefficient is 81, not 18

Wrong \$ 18 (x^2) (y^2) \$

10

Choice-B

This choice is incorrect, the coefficient should be 81, not 181, and the exponent of y is positive, not negative

Wrong \$ 181 (x^2) (y^-2) \$

11

Choice-C

This choice is incorrect, the coefficient should be 81, not 92, and the exponent of y is 2, not 3

Wrong \$ 92 (x^2) (y^3) \$

12

Choice-D

This option matches the simplified expression \$ 81(x^2) (y^2)\$

Correct \$ 81 (x^2) (y^2) \$

13

Step

Option

D

14

Sumup

Please Summarize Choices