1

Problem

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

2

Step

The given expression is

\$ (3xy)^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: \$ 3^2 \times (xy)^2 \$.

5

Step

Simplify each part:

\$ 3^2 = 3 \times 3 = 9\$

\$ (xy)^2 = x^2 \times y^2 \$

6

Step

Combine the simplified parts:

\$9 \times x^2 \times y^2 \$

7

Solution

So, the simplified expression is So, the simplified expression is \$9 \times x^2 \times y^2\$.

8

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

9

Choice-A

This is the correct simplification because \$(3xy)^2 = 9 \times x^2 \times y^2\$

Correct \$ 9 (x^2) (y^2) \$

10

Choice-B

This is incorrect because it has an incorrect coefficient of 6, and the exponents of x and y are not squared

Wrong \$ 6 (x^-2) (y^2) \$

11

Choice-C

This is incorrect because it has an incorrect coefficient of 8, and the exponent of y is squared, but the exponent of x is not

Wrong \$ 8 (x^2) (y^-2) \$

12

Choice-D

This is incorrect because it has a negative sign, and the correct coefficient should be positive

Wrong \$ -9 (x^2) (y^2) \$

13

Step

Option

A

14

Sumup

Please Summarize Choices