Multiply Powers with Same Base: Solving 4² × 4⁴

Q: Why do I add the exponents instead of multiplying them?

Because $ 4^2 \times 4^4 $ means (4×4) × (4×4×4×4). When you count all the 4's being multiplied together, you get 6 total 4's, which equals $ 4^6 $!

Q: What if the bases are different numbers?

The rule only works when bases are the same! For example, $ 3^2 \times 4^3 $ cannot be simplified using this rule. You'd have to calculate each power separately first.

Q: Does this work with negative exponents too?

Yes! The same rule applies: $ 4^{-1} \times 4^3 = 4^{-1+3} = 4^2 $. Just remember to add the exponents, even if one is negative.

Q: How can I remember this rule easily?

Think of it as "same base, add the powers". You can also remember that exponents tell you how many times to multiply the base, so combining them means adding those counts together.

Q: What's the difference between this and raising a power to a power?

Great question! $ 4^2 \times 4^4 $ uses addition (multiply powers = add exponents), but $ (4^2)^4 $ uses multiplication (power of a power = multiply exponents) to get $ 4^8 $.

Exponent Rules with Multiplication Properties

$4^2\times4^4=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 When multiplying powers with the same base,

00:10 add the exponents together. For example, the answer is six.

00:14 And that's how we solve it!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$4^2\times4^4=$

Step-by-step solution

To solve the exercise we use the property of multiplication of powers with the same bases:

$a^n * a^m = a^{n+m}$

With the help of this property, we can add the exponents.

$4^2\times4^4=4^{4+2}=4^6$

Final Answer

$4^6$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying powers with same base, add the exponents
Technique: $4^2 \times 4^4 = 4^{2+4} = 4^6$
Check: Verify by calculating: $16 \times 256 = 4096 = 4^6$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying the exponents instead of adding them
Don't multiply exponents like $4^2 \times 4^4 = 4^8$ = wrong answer! This confuses multiplication with exponentiation rules. Always add exponents when multiplying powers with the same base.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why do I add the exponents instead of multiplying them?

Because $4^2 \times 4^4$ means (4×4) × (4×4×4×4). When you count all the 4's being multiplied together, you get 6 total 4's, which equals $4^6$ !

What if the bases are different numbers?

The rule only works when bases are the same! For example, $3^2 \times 4^3$ cannot be simplified using this rule. You'd have to calculate each power separately first.

Does this work with negative exponents too?

Yes! The same rule applies: $4^{-1} \times 4^3 = 4^{-1+3} = 4^2$ . Just remember to add the exponents, even if one is negative.

How can I remember this rule easily?

Think of it as "same base, add the powers". You can also remember that exponents tell you how many times to multiply the base, so combining them means adding those counts together.

What's the difference between this and raising a power to a power?

Great question! $4^2 \times 4^4$ uses addition (multiply powers = add exponents), but $(4^2)^4$ uses multiplication (power of a power = multiply exponents) to get $4^8$ .

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