Solve (4×9×11)^a: Finding the Power of a Product

Q: Why do I need to apply the exponent to each factor separately?

The power law states that $ (a×b×c)^n = a^n×b^n×c^n $. This works because when you multiply the same expression 'n' times, each factor appears 'n' times in the multiplication.

Q: What if I first multiply the numbers inside parentheses?

While $ 4×9×11 = 396 $ gives you $ 396^a $, this isn't the simplified form the question asks for. The distributed form $ 4^a×9^a×11^a $ shows the power property clearly.

Q: Does this work with any number of factors?

Yes! Whether you have 2 factors like $ (x×y)^n $ or 10 factors, the exponent distributes to every single factor inside the parentheses.

Q: Can I use this rule backwards too?

Absolutely! If you see $ 3^5×7^5×2^5 $, you can factor it as $ (3×7×2)^5 $. This reverse power law helps simplify expressions.

Q: What if the exponent is a fraction or negative?

The power law works with any exponent! Whether 'a' is positive, negative, fractional, or even irrational, you still distribute it to each factor: $ (4×9×11)^{-2} = 4^{-2}×9^{-2}×11^{-2} $.

Power Properties with Multiple Factors

Solve the following exercise:

$(4\times9\times11)^a$

❤️ 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

00:07 Let's begin!

00:10 We'll use the formula for powers with products.

00:13 When a product is raised to a power, say N,

00:17 each factor is also raised to that same power, N.

00:22 We're using this idea in our exercise.

00:25 Let's expand the brackets and apply the power to each factor.

00:29 And that's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$(4\times9\times11)^a$

Step-by-step solution

We use the power law for a multiplication between parentheses:

$(z\cdot t)^n=z^n\cdot t^n$

That is, a power applied to a multiplication between parentheses is applied to each term when the parentheses are opened,

We apply it in the problem:

$(4\cdot9\cdot11)^a=4^a\cdot9^a\cdot11^a$

Therefore, the correct answer is option b.

Note:

From the power property formula mentioned, we can understand that it works not only with two terms of the multiplication between parentheses, but also valid with a multiplication between multiple terms in parentheses. As we can see in this problem.

Final Answer

$4^a\times9^a\times11^a$

Key Points to Remember

Essential concepts to master this topic

Power Law: Distribute the exponent to each factor inside parentheses
Technique: Transform $(4×9×11)^a$ to $4^a×9^a×11^a$
Check: Each factor gets the same exponent 'a' when distributed ✓

Common Mistakes

Avoid these frequent errors

Only applying the exponent to one or some factors
Don't leave some factors without the exponent like $4^a×9×11$ = wrong distribution! This violates the power law and creates incorrect expressions. Always apply the exponent to every single factor inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

Choose the expression that corresponds to the following:

$$ $\left(2\times11\right)^5=$

FAQ

Everything you need to know about this question

Why do I need to apply the exponent to each factor separately?

The power law states that $(a×b×c)^n = a^n×b^n×c^n$ . This works because when you multiply the same expression 'n' times, each factor appears 'n' times in the multiplication.

What if I first multiply the numbers inside parentheses?

While $4×9×11 = 396$ gives you $396^a$ , this isn't the simplified form the question asks for. The distributed form $4^a×9^a×11^a$ shows the power property clearly.

Does this work with any number of factors?

Yes! Whether you have 2 factors like $(x×y)^n$ or 10 factors, the exponent distributes to every single factor inside the parentheses.

Can I use this rule backwards too?

Absolutely! If you see $3^5×7^5×2^5$ , you can factor it as $(3×7×2)^5$ . This reverse power law helps simplify expressions.

What if the exponent is a fraction or negative?

The power law works with any exponent! Whether 'a' is positive, negative, fractional, or even irrational, you still distribute it to each factor: $(4×9×11)^{-2} = 4^{-2}×9^{-2}×11^{-2}$ .

🌟 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

Solve (4×9×11)^a: Finding the Power of a Product

Power Properties with Multiple Factors

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to apply the exponent to each factor separately?

What if I first multiply the numbers inside parentheses?

Does this work with any number of factors?

Can I use this rule backwards too?

What if the exponent is a fraction or negative?

🌟 Unlock Your Math Potential

More Questions

Exponents Rules

Calculate the Area: Four x-cm Squares at y-cm Square Vertices

Simplify (4^x)^y: Solving Double Exponent Expressions

Solve (x²×3)²: Step-by-Step Double Square Calculation

Solve (a⁵)⁷: Simplifying Power of Power Expressions

Applying Combined Exponents Rules

Solve: 2^3 × 2^4 + (4^3)^2 + 2^5/2^3 - Complete Exponent Expression

Solve: (8x⁷y³/20) × (4/2x⁵y²) - Fraction Multiplication with Variables

Extract the Common Factor from 4x³+8x⁴: Step-by-Step Solution

Solve (g×a×x)⁴ + (4^a)^x: Complex Exponential Expression Challenge

Power of a Product

Calculate (3×4×5)⁴: Fourth Power of a Triple Product

Calculate (4×7×3)²: Product of Three Numbers Squared