Solve: 3² × y² Expression (Multiplying Squared Terms)

Exponent Rules with Product Simplification

Insert the corresponding expression:

32×y2= 3^2\times y^2=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simplify the following problem
00:03 A product where each factor is raised to the power of that factor (N)
00:07 Can be converted to parentheses of the entire product raised to the power of the factor (N)
00:12 We will apply this formula to our exercise
00:18 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Insert the corresponding expression:

32×y2= 3^2\times y^2=

2

Step-by-step solution

To solve the problem 32×y2= 3^2 \times y^2 = , we will make use of the power of a product rule, which helps simplify products with the same exponents.

The rule states that for any numbers a a and b b and any exponent m m , (am×bm)=(a×b)m(a^m \times b^m) = (a \times b)^m.

Using this rule, we can combine 32 3^2 and y2 y^2 into a single expression:

  • Identify the bases: We have a base of 3 and a base of y y , both raised to the power of 2.

  • Apply the formula, combining the bases under a common exponent: (3×y)2(3 \times y)^2.

This shows that 32×y2=(3×y)2 3^2 \times y^2 = \left(3 \times y\right)^2 .

3

Final Answer

(3×y)2 \left(3\times y\right)^2

Key Points to Remember

Essential concepts to master this topic
  • Power Rule: Same exponents can combine using am×bm=(a×b)m a^m \times b^m = (a \times b)^m
  • Technique: Combine 32×y2 3^2 \times y^2 into (3×y)2 (3 \times y)^2 since both have exponent 2
  • Check: Expand back: (3y)2=32×y2=9y2 (3y)^2 = 3^2 \times y^2 = 9y^2 ✓

Common Mistakes

Avoid these frequent errors
  • Adding exponents instead of using product rule
    Don't write 32×y2=(3y)4 3^2 \times y^2 = (3y)^4 by adding 2+2=4! This confuses the product rule with the power rule. The exponents stay the same when bases are different. Always use am×bm=(a×b)m a^m \times b^m = (a \times b)^m when exponents match.

Practice Quiz

Test your knowledge with interactive questions

\( (4^2)^3+(g^3)^4= \)

FAQ

Everything you need to know about this question

When can I combine terms with exponents like this?

+

You can only combine when the exponents are identical! If you have 32×y3 3^2 \times y^3 , you cannot simplify further because the exponents 2 and 3 are different.

Why isn't the answer (9y)2 (9y)^2 ?

+

Don't calculate 32=9 3^2 = 9 first! The rule works with the original bases. Keep it as (3×y)2 (3 \times y)^2 to show the proper application of am×bm=(a×b)m a^m \times b^m = (a \times b)^m .

What's the difference between this and 32+y2 3^2 + y^2 ?

+

Huge difference! Addition cannot be combined this way - 32+y2 3^2 + y^2 stays as is. Only multiplication of same exponents can use the product rule.

How do I remember when to use this rule?

+

Look for multiplication (×) and matching exponents. If you see both, you can combine the bases under one exponent: am×bm=(ab)m a^m \times b^m = (ab)^m

Can this work with more than two terms?

+

Yes! For example: 23×x3×y3=(2xy)3 2^3 \times x^3 \times y^3 = (2xy)^3 . As long as all exponents match, you can combine any number of terms.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Exponents Rules questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Power of a Product

Reduce the Expression: Product of a⁸ × b⁸ × c⁸
Click to solve
Simplify the Product: 3^(5x+1/2) × 7^(5x+1/2) × 5^(5x+1/2)
Click to solve