Simplify Powers: 2^4 × 2^-2 × 2^3 Using Exponent Rules

Q: Why do we add exponents when multiplying powers?

Think of it this way: $ 2^4 $ means 2 × 2 × 2 × 2, and $ 2^3 $ means 2 × 2 × 2. When you multiply them together, you get 7 total factors of 2, which is $ 2^7 $!

Q: What if I get confused with the signs?

Write it out step by step: 4 + (-2) + 3. First do 4 + (-2) = 4 - 2 = 2. Then add 3: 2 + 3 = 5. So the answer is $ 2^5 $.

Q: Can I use this rule with different bases?

No! This rule only works when all bases are the same. You cannot add exponents for $ 2^3 \times 3^4 $ because the bases (2 and 3) are different.

Q: Should I calculate the final numerical answer?

It depends on what the question asks! If it says "simplify" or "reduce," then $ 2^5 $ is the perfect answer. If it asks to "evaluate," then calculate $ 2^5 = 32 $.

Exponent Rules with Negative Powers

Reduce the following equation:

$2^4\times2^{-2}\times2^3=$

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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)

00:06 equals the same base raised to the sum of the exponents (N+M)

00:10 We will apply this formula to our exercise

00:14 Note that we are adding a negative factor

00:19 A positive x A negative is always negative, so we perform a subtraction

00:28 Let's continue to solve the problem

00:38 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Reduce the following equation:

$2^4\times2^{-2}\times2^3=$

Step-by-step solution

To solve this problem, we'll apply the rule for multiplying powers with the same base:

Step 1: Recognize that all terms share the base 2.
Step 2: Apply the multiplication rule for exponents: $2^m \times 2^n = 2^{m+n}$ .
Step 3: Combine the exponents: $2^{4} \times 2^{-2} \times 2^{3}$ becomes $2^{4 + (-2) + 3}$ .

According to the provided choices, the reduced expression using the property is $2^{4-2+3}$ , which aligns with choice 1.

Final Answer

$2^{4-2+3}$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying same bases, add all exponents together
Technique: $2^4 \times 2^{-2} \times 2^3 = 2^{4+(-2)+3}$
Check: Calculate final exponent: 4 + (-2) + 3 = 5, so answer is $2^5 = 32$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying exponents instead of adding them
Don't multiply the exponents like 4 × (-2) × 3 = -24! This gives $2^{-24}$ which is completely wrong. When multiplying same bases, always add the exponents: 4 + (-2) + 3 = 5.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why do we add exponents when multiplying powers?

Think of it this way: $2^4$ means 2 × 2 × 2 × 2, and $2^3$ means 2 × 2 × 2. When you multiply them together, you get 7 total factors of 2, which is $2^7$ !

How do I handle negative exponents in this rule?

Treat negative exponents just like any other number when adding! So $2^4 \times 2^{-2}$ becomes $2^{4+(-2)} = 2^2$ . Remember: adding a negative is the same as subtracting.

What if I get confused with the signs?

Write it out step by step: 4 + (-2) + 3. First do 4 + (-2) = 4 - 2 = 2. Then add 3: 2 + 3 = 5. So the answer is $2^5$ .

Can I use this rule with different bases?

No! This rule only works when all bases are the same. You cannot add exponents for $2^3 \times 3^4$ because the bases (2 and 3) are different.

Should I calculate the final numerical answer?

It depends on what the question asks! If it says "simplify" or "reduce," then $2^5$ is the perfect answer. If it asks to "evaluate," then calculate $2^5 = 32$ .

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