Complete the Expression: Finding (5×b×a)⁴

Q: Why does every factor get the exponent?

The Power of Product Rule says when you raise a product to an exponent, it's like multiplying the entire expression by itself 4 times. So $ (5ba)^4 = (5ba) \times (5ba) \times (5ba) \times (5ba) $!

Q: What if there are more factors inside the parentheses?

Every single factor gets the exponent! Whether you have 2 factors or 10 factors, the rule stays the same - each one gets raised to the power.

Q: Do I multiply the exponents or add them?

Neither! You apply the same exponent to each factor separately. Don't change the exponent number - just put it on each factor: $ 5^4, b^4, a^4 $.

Q: Can I rearrange the factors in my answer?

Yes! Multiplication is commutative, so $ 5^4 \times b^4 \times a^4 $ equals $ a^4 \times 5^4 \times b^4 $. The order doesn't matter.

Power of Product with Mixed Variables

Insert the corresponding expression:

$\left(5\times b\times a\right)^4=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the following problem

00:03 In order to open parentheses with a multiplication operation and an outside exponent

00:08 Raise each factor to the power

00:14 We will apply this formula to our exercise

00:26 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Insert the corresponding expression:

$\left(5\times b\times a\right)^4=$

Step-by-step solution

To solve the expression $\left(5 \times b \times a\right)^4$ , we'll apply the Power of a Product Rule, which states that when a product is raised to an exponent, each factor in the product is raised to that exponent individually.

First, identify each factor in the product: $5$ , $b$ , and $a$ .
Next, apply the exponent to each factor:
- The number $5$ becomes $5^4$ .
- The variable $b$ becomes $b^4$ .
- The variable $a$ becomes $a^4$ .
Finally, multiply these results together to obtain the simplified expression.

Therefore, the expression $\left(5 \times b \times a\right)^4$ simplifies to $5^4 \times b^4 \times a^4$ , which corresponds to Choice 3.

Final Answer

$5^4\times b^4\times a^4$

Key Points to Remember

Essential concepts to master this topic

Rule: Each factor gets raised to the exponent individually
Technique: $(5 \times b \times a)^4 = 5^4 \times b^4 \times a^4$
Check: Count factors: 3 factors in, 3 factors out with exponent 4 ✓

Common Mistakes

Avoid these frequent errors

Only applying exponent to one factor
Don't raise just one factor to the 4th power like $5^4 \times b \times a$ = wrong answer! This ignores the Power of Product Rule. Always apply the exponent to every single factor in the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why does every factor get the exponent?

The Power of Product Rule says when you raise a product to an exponent, it's like multiplying the entire expression by itself 4 times. So $(5ba)^4 = (5ba) \times (5ba) \times (5ba) \times (5ba)$ !

What if there are more factors inside the parentheses?

Every single factor gets the exponent! Whether you have 2 factors or 10 factors, the rule stays the same - each one gets raised to the power.

Do I multiply the exponents or add them?

Neither! You apply the same exponent to each factor separately. Don't change the exponent number - just put it on each factor: $5^4, b^4, a^4$ .

Can I rearrange the factors in my answer?

Yes! Multiplication is commutative, so $5^4 \times b^4 \times a^4$ equals $a^4 \times 5^4 \times b^4$ . The order doesn't matter.

What if one factor is negative?

The negative sign stays with its factor and gets raised to the power too. Remember: $(-3)^4$ is positive, but $(-3)^3$ is negative!

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