Simplify the Expression: Division of x^18 by x^7

Q: Why do we subtract exponents when dividing?

Think of it as canceling out common factors! $ \frac{x^{18}}{x^7} $ means you have 18 x's on top and 7 x's on bottom. Cancel 7 from each, leaving 11 x's on top: $ x^{11} $.

Q: What if the bottom exponent is bigger than the top?

You still subtract! For example, $ \frac{x^5}{x^8} = x^{5-8} = x^{-3} $. The negative exponent means the result goes in the denominator: $ \frac{1}{x^3} $.

Q: Can I use this rule with different bases like x and y?

No! This rule only works when the bases are exactly the same. $ \frac{x^5}{y^3} $ cannot be simplified using this rule because x and y are different.

Q: How do I remember which operation to use?

Use this memory trick: Same operation, opposite rule. When you multiply same bases, you add exponents. When you divide same bases, you subtract exponents!

Q: What does the final answer x^11 actually mean?

$ x^{11} $ means x multiplied by itself 11 times. It's the result of dividing $ x^{18} $ (18 x's) by $ x^7 $ (7 x's), leaving 11 x's.

Exponent Division with Same Bases

Insert the corresponding expression:

$\frac{x^{18}}{x^7}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:02 We'll use the formula for dividing powers

00:04 Any number (A) to the power of (N) divided by the same base (A) to the power of (M)

00:06 equals the number (A) to the power of the difference of exponents (M-N)

00:08 We'll use this formula in our exercise

00:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Insert the corresponding expression:

$\frac{x^{18}}{x^7}=$

Step-by-step solution

We are given the expression: $\frac{x^{18}}{x^7}$ .

To simplify this, we use the Power of a Quotient Rule for Exponents. This rule states that when dividing like bases, you subtract the exponent in the denominator from the exponent in the numerator.

So, according to this rule:
$\frac{x^m}{x^n} = x^{m-n}$ .

Apply this rule to our expression: $\frac{x^{18}}{x^7} = x^{18-7}$ .

Simplify the exponent by subtracting: $18-7 = 11$ .

Therefore, the simplified expression is: $x^{11}$ .

However, the expected form of the answer once applying the rule (before simplification) is: $x^{18-7}$ .

The solution to the question is: $x^{18-7}$ .

Final Answer

$x^{18-7}$

Key Points to Remember

Essential concepts to master this topic

Rule: When dividing same bases, subtract the exponents
Technique: $\frac{x^{18}}{x^7} = x^{18-7}$ becomes $x^{11}$
Check: Multiply back: $x^{11} \times x^7 = x^{18}$ ✓

Common Mistakes

Avoid these frequent errors

Adding or multiplying exponents instead of subtracting
Don't add (18+7) or multiply (18×7) the exponents = wrong answer like $x^{25}$ or $x^{126}$ ! This confuses division with multiplication rules. Always subtract exponents when dividing same bases.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why do we subtract exponents when dividing?

Think of it as canceling out common factors! $\frac{x^{18}}{x^7}$ means you have 18 x's on top and 7 x's on bottom. Cancel 7 from each, leaving 11 x's on top: $x^{11}$ .

What if the bottom exponent is bigger than the top?

You still subtract! For example, $\frac{x^5}{x^8} = x^{5-8} = x^{-3}$ . The negative exponent means the result goes in the denominator: $\frac{1}{x^3}$ .

Can I use this rule with different bases like x and y?

No! This rule only works when the bases are exactly the same. $\frac{x^5}{y^3}$ cannot be simplified using this rule because x and y are different.

How do I remember which operation to use?

Use this memory trick: Same operation, opposite rule. When you multiply same bases, you add exponents. When you divide same bases, you subtract exponents!

What does the final answer x^11 actually mean?

$x^{11}$ means x multiplied by itself 11 times. It's the result of dividing $x^{18}$ (18 x's) by $x^7$ (7 x's), leaving 11 x's.

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