Math Problem Statement

Simplify (-3ab)^2.

Solution

The problem in the image asks to simplify the expression (3ab)2(-3ab)^2.

Let's go through the steps to simplify this expression:

  1. Start by applying the power rule, which states that (xy)n=xnyn(xy)^n = x^n y^n for any terms xx, yy, and exponent nn. (3ab)2=(3)2(a)2(b)2(-3ab)^2 = (-3)^2 \cdot (a)^2 \cdot (b)^2

  2. Calculate each term separately: (3)2=9,a2=a2,b2=b2(-3)^2 = 9, \quad a^2 = a^2, \quad b^2 = b^2

  3. Multiply everything together: (3ab)2=9a2b2(-3ab)^2 = 9a^2b^2

Thus, the simplified form of (3ab)2(-3ab)^2 is 9a2b29a^2b^2.

Would you like any further details or have any questions?

Here are 5 related questions you might find useful:

  1. How would you simplify (4xy)3(-4xy)^3?
  2. What is the general rule for raising a product to a power?
  3. Can you simplify (2a3b)2(2a^3b)^2?
  4. How does raising a negative number to an even power affect the result?
  5. What is the difference between raising a term to an odd versus an even power?

Tip: When simplifying expressions, apply the exponent to each factor in the parentheses separately.

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Math Problem Analysis

Mathematical Concepts

Exponents
Algebra

Formulas

(xy)^n = x^n * y^n

Theorems

Power of a product rule

Suitable Grade Level

Grades 7-9