Simplify the Product: 2¹ × 2² × 2³ Using Exponent Rules

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

When you multiply powers with the same base, you're essentially combining repeated multiplication. $ 2^1 \times 2^2 \times 2^3 $ means 2 × (2×2) × (2×2×2), which gives you six 2's total: $ 2^6 $!

Q: What if the bases are different, like $ 2^3 \times 3^2 $ ?

You cannot combine exponents when bases are different! $ 2^3 \times 3^2 $ must be calculated as 8 × 9 = 72. The addition rule only works with identical bases.

Q: How do I remember this rule?

Think of exponents as counting how many times the base appears. When multiplying, you're adding more copies of the base, so you add the counts (exponents)!

Q: Should I calculate $ 1+2+3 $ right away?

The question asks for the simplified form, which is $ 2^{1+2+3} $. You can calculate $ 1+2+3=6 $ to get $ 2^6 $, but both forms show you applied the rule correctly!

Q: What's the difference between $ 2^6 $ and $ 2^{1+2+3} $ ?

They're mathematically identical! $ 2^{1+2+3} $ shows your work clearly, while $ 2^6 $ is the final simplified form. Both demonstrate understanding of exponent rules.

Exponent Rules with Same Base Multiplication

Simplify the following equation:

$2^1\times2^2\times2^3=$

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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 According to the laws of exponents, the multiplication of powers with an equal base (A)

00:08 equals the same base raised to the sum of the exponents (N+M)

00:12 We will apply this formula to our exercise

00:17 We'll maintain the base and add together the exponents

00:29 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the following equation:

$2^1\times2^2\times2^3=$

Step-by-step solution

To simplify the expression $2^1 \times 2^2 \times 2^3$ , we'll apply the rule for multiplying powers with the same base:

When multiplying powers with the same base, you add the exponents.

Let's apply this to our expression:

$2^1 \times 2^2 \times 2^3 = 2^{1+2+3}$

Now, calculate the sum of the exponents: $1 + 2 + 3 = 6$ .

Thus, the expression simplifies to

$2^6$ .

By comparing it with the given choices, the correct simplified form, $2^{1+2+3}$ , corresponds to choice 2:
$2^{1+2+3}$ .

Final Answer

$2^{1+2+3}$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying same bases, add the exponents together
Technique: $2^1 \times 2^2 \times 2^3 = 2^{1+2+3}$ before calculating
Check: Verify $2^6 = 64$ equals $2 \times 4 \times 8 = 64$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying the exponents instead of adding them
Don't calculate $2^{1 \times 2 \times 3} = 2^6$ by multiplying exponents = wrong method! This confuses the power rule with the product rule. Always add exponents when multiplying same bases: $2^{1+2+3}$ .

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?

When you multiply powers with the same base, you're essentially combining repeated multiplication. $2^1 \times 2^2 \times 2^3$ means 2 × (2×2) × (2×2×2), which gives you six 2's total: $2^6$ !

What if the bases are different, like $2^3 \times 3^2$ ?

You cannot combine exponents when bases are different! $2^3 \times 3^2$ must be calculated as 8 × 9 = 72. The addition rule only works with identical bases.

How do I remember this rule?

Think of exponents as counting how many times the base appears. When multiplying, you're adding more copies of the base, so you add the counts (exponents)!

Should I calculate $1+2+3$ right away?

The question asks for the simplified form, which is $2^{1+2+3}$ . You can calculate $1+2+3=6$ to get $2^6$ , but both forms show you applied the rule correctly!

What's the difference between $2^6$ and $2^{1+2+3}$ ?

They're mathematically identical! $2^{1+2+3}$ shows your work clearly, while $2^6$ is the final simplified form. Both demonstrate understanding of exponent rules.

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Simplify the Product: 2¹ × 2² × 2³ Using Exponent Rules

Exponent Rules with Same Base Multiplication

❤️ 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 add the exponents instead of multiplying them?

What if the bases are different, like $2^3 \times 3^2$ ?

How do I remember this rule?

Should I calculate $1+2+3$ right away?

What's the difference between $2^6$ and $2^{1+2+3}$ ?

🌟 Unlock Your Math Potential

More Questions

Multiplication of Powers

Simplify Powers of 10: 10^5 × 10^7 × 10^2 Step by Step

Simplify 13³ × 13⁴ × 13²: Multiplying Powers with Same Base

Multiply Powers of 11: Simplifying 11²×11³×11⁴

Simplify the Expression: 9^7 × 9^3 × 9^5 Using Exponent Rules

Simplify the Product: 2¹ × 2² × 2³ Using Exponent Rules

Exponent Rules with Same Base Multiplication

❤️ 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 add the exponents instead of multiplying them?

What if the bases are different, like 23×32 2^3 \times 3^2 23×32?

How do I remember this rule?

Should I calculate 1+2+3 1+2+3 1+2+3 right away?

What's the difference between 26 2^6 26 and 21+2+3 2^{1+2+3} 21+2+3?

🌟 Unlock Your Math Potential

More Questions

Multiplication of Powers

Simplify Powers of 10: 10^5 × 10^7 × 10^2 Step by Step

Simplify 13³ × 13⁴ × 13²: Multiplying Powers with Same Base

Multiply Powers of 11: Simplifying 11²×11³×11⁴

Simplify the Expression: 9^7 × 9^3 × 9^5 Using Exponent Rules

What if the bases are different, like $2^3 \times 3^2$ ?

Should I calculate $1+2+3$ right away?

What's the difference between $2^6$ and $2^{1+2+3}$ ?