Simplify the Expression: x^8 × x^7 × x^10 Using Exponent Rules

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

The multiplication rule for exponents states $ a^m \times a^n = a^{m+n} $. Think of it this way: $ x^3 \times x^2 $ means (x·x·x) × (x·x) which gives you 5 x's total, so $ x^5 $!

Q: What if the bases are different, like $ x^5 \times y^3 $ ?

You cannot combine exponents when the bases are different! $ x^5 \times y^3 $ stays as $ x^5y^3 $. The rule only works with identical bases.

Q: How do I handle more than three terms with exponents?

The same rule applies! Just add all the exponents together. For example: $ x^2 \times x^4 \times x^1 \times x^6 = x^{2+4+1+6} = x^{13} $.

Q: What's the difference between $ (x^8)^7 $ and $ x^8 \times x^7 $ ?

$ (x^8)^7 $ uses the power rule where you multiply exponents: $ (x^8)^7 = x^{8 \times 7} = x^{56} $. But $ x^8 \times x^7 $ uses the product rule where you add exponents: $ x^{8+7} = x^{15} $.

Q: Can I double-check my work somehow?

Yes! Try substituting a simple number like x = 2. For our problem: $ 2^8 \times 2^7 \times 2^{10} $ should equal $ 2^{25} $. Use a calculator to verify both sides give the same huge number!

Exponent Rules with Multiple Base Products

Reduce the following equation:

$x^8\times x^7\times x^{10}=$

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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 equal bases (A)

00:09 equals the same base raised to the sum of the exponents (N+M)

00:14 We will apply this formula to our exercise

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

00:42 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:

$x^8\times x^7\times x^{10}=$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify the exponents in the expression $x^8 \times x^7 \times x^{10}$ . They are 8, 7, and 10.
Step 2: Apply the multiplication rule for exponents, which states $a^m \times a^n = a^{m+n}$ .
Here, it becomes: $x^8 \times x^7 \times x^{10} = x^{8+7+10}$ .
Step 3: Simplify the expression by adding the exponents together:

After performing the addition, $8 + 7 + 10 = 25$ .

Thus, the reduced form of the equation is $x^{25}$ .

Therefore, the final answer is $x^{25}$ .

Final Answer

$x^{25}$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying same bases, add the exponents together
Technique: $x^8 \times x^7 \times x^{10} = x^{8+7+10} = x^{25}$
Check: Count exponents: 8, 7, 10 then verify 8+7+10=25 ✓

Common Mistakes

Avoid these frequent errors

Multiplying the exponents instead of adding them
Don't calculate $x^{8 \times 7 \times 10} = x^{560}$ ! This confuses the multiplication rule with the power rule and gives a massively wrong answer. Always add exponents when multiplying same bases: $x^8 \times x^7 \times x^{10} = x^{8+7+10} = x^{25}$ .

Practice Quiz

Test your knowledge with interactive questions

$(3\times4\times5)^4=$

FAQ

Everything you need to know about this question

Why do I add the exponents instead of multiplying them?

The multiplication rule for exponents states $a^m \times a^n = a^{m+n}$ . Think of it this way: $x^3 \times x^2$ means (x·x·x) × (x·x) which gives you 5 x's total, so $x^5$ !

What if the bases are different, like $x^5 \times y^3$ ?

You cannot combine exponents when the bases are different! $x^5 \times y^3$ stays as $x^5y^3$ . The rule only works with identical bases.

How do I handle more than three terms with exponents?

The same rule applies! Just add all the exponents together. For example: $x^2 \times x^4 \times x^1 \times x^6 = x^{2+4+1+6} = x^{13}$ .

What's the difference between $(x^8)^7$ and $x^8 \times x^7$ ?

$(x^8)^7$ uses the power rule where you multiply exponents: $(x^8)^7 = x^{8 \times 7} = x^{56}$ . But $x^8 \times x^7$ uses the product rule where you add exponents: $x^{8+7} = x^{15}$ .

Can I double-check my work somehow?

Yes! Try substituting a simple number like x = 2. For our problem: $2^8 \times 2^7 \times 2^{10}$ should equal $2^{25}$ . Use a calculator to verify both sides give the same huge number!

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Simplify the Expression: x^8 × x^7 × x^10 Using Exponent Rules

Exponent Rules with Multiple Base Products

❤️ 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 $x^5 \times y^3$ ?

How do I handle more than three terms with exponents?

What's the difference between $(x^8)^7$ and $x^8 \times x^7$ ?

Can I double-check my work somehow?

🌟 Unlock Your Math Potential

More Questions

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Simplify the Expression: a² × a³ Using Power Rules

Simplify the Expression: x^8 × x^7 × x^10 Using Exponent Rules

Exponent Rules with Multiple Base Products

❤️ 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 x5×y3 x^5 \times y^3 x5×y3?

How do I handle more than three terms with exponents?

What's the difference between (x8)7 (x^8)^7 (x8)7 and x8×x7 x^8 \times x^7 x8×x7?

Can I double-check my work somehow?

🌟 Unlock Your Math Potential

More Questions

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Simplify the Expression: y^2 · y^3 · y^6 Using Exponent Rules

Simplify the Expression: b^9 × b^4 × b^5 Using Exponent Rules

Simplify b⁴ × b⁵: Exponent Multiplication Practice

Simplify the Expression: a² × a³ Using Power Rules

What if the bases are different, like $x^5 \times y^3$ ?

What's the difference between $(x^8)^7$ and $x^8 \times x^7$ ?