Reduce the Expression: x³ × x⁴ × x⁸ Using Exponent Rules

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

Because exponents represent repeated multiplication! $ x^3 $ means x·x·x, so $ x^3 \times x^4 $ means (x·x·x)·(x·x·x·x) = x·x·x·x·x·x·x = $ x^7 $.

Q: What if the bases are different, like x^3 × y^4?

The product rule only works with the same base! When bases are different, you cannot combine them. $ x^3 \times y^4 $ stays as $ x^3y^4 $.

Q: How is this different from (x^3)^4?

That uses the power rule, not the product rule! $ (x^3)^4 $ means multiply exponents: 3×4 = 12, so $ x^{12} $. But $ x^3 \times x^4 $ means add exponents: 3+4 = 7.

Q: Can I use this rule with more than two terms?

Absolutely! The product rule works for any number of terms with the same base. Just keep adding all the exponents: $ x^2 \times x^5 \times x^1 \times x^3 = x^{2+5+1+3} = x^{11} $.

Exponent Multiplication with Multiple Terms

Reduce the following equation:

$x^3\times x^4\times x^8=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the following problem

00:04 According to the laws of exponents, multiplying exponents with the same base (A)

00:07 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 We'll maintain the base and add the exponents together

00:25 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:

$x^3\times x^4\times x^8=$

Final Answer

A'+C' are correct

Key Points to Remember

Essential concepts to master this topic

Product Rule: When multiplying same bases, add the exponents together
Technique: $x^3 \times x^4 \times x^8 = x^{3+4+8} = x^{15}$
Check: Count total factors: x·x·x·x·x·x·x·x·x·x·x·x·x·x·x = x^15 ✓

Common Mistakes

Avoid these frequent errors

Multiplying exponents instead of adding them
Don't multiply 3×4×8 = 96 to get x^96! This confuses the product rule with the power rule and gives a completely wrong answer. Always add exponents when multiplying same bases: 3+4+8 = 15.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why do I add exponents instead of multiplying them?

Because exponents represent repeated multiplication! $x^3$ means x·x·x, so $x^3 \times x^4$ means (x·x·x)·(x·x·x·x) = x·x·x·x·x·x·x = $x^7$ .

What if the bases are different, like x^3 × y^4?

The product rule only works with the same base! When bases are different, you cannot combine them. $x^3 \times y^4$ stays as $x^3y^4$ .

How is this different from (x^3)^4?

That uses the power rule, not the product rule! $(x^3)^4$ means multiply exponents: 3×4 = 12, so $x^{12}$ . But $x^3 \times x^4$ means add exponents: 3+4 = 7.

Can I use this rule with more than two terms?

Absolutely! The product rule works for any number of terms with the same base. Just keep adding all the exponents: $x^2 \times x^5 \times x^1 \times x^3 = x^{2+5+1+3} = x^{11}$ .

What if one of the exponents is negative?

The same rule applies! Just add the exponents normally. For example: $x^3 \times x^{-2} = x^{3+(-2)} = x^1 = x$ . Negative exponents don't change the addition rule.

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