Simplify y^20 ÷ y^11: Laws of Exponents Practice

Q: Why do we subtract exponents when dividing?

Think of it this way: $ \frac{y^{20}}{y^{11}} $ means you have 20 y's multiplied together, then you're dividing by 11 y's. The 11 y's cancel out, leaving you with $ 20 - 11 = 9 $ y's remaining!

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

You still subtract! For example: $ \frac{y^5}{y^8} = y^{5-8} = y^{-3} $. The negative exponent means one over that positive power: $ \frac{1}{y^3} $.

Q: Does this work with different bases like x and y?

No! The quotient rule only works when the bases are exactly the same. You cannot simplify $ \frac{x^5}{y^3} $ using this rule because x and y are different variables.

Q: Can I use this rule with numbers too?

Absolutely! $ \frac{3^7}{3^4} = 3^{7-4} = 3^3 = 27 $. The quotient rule works with any base as long as it's the same on top and bottom.

Q: What's the difference between this and multiplying exponents?

When you multiply same bases, you add exponents: $ y^5 \times y^3 = y^8 $. When you divide same bases, you subtract exponents: $ \frac{y^5}{y^3} = y^2 $.

Quotient Rule with Same Base Variables

Insert the corresponding expression:

$\frac{y^{20^{}}}{y^{11}}=$

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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 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:

$\frac{y^{20^{}}}{y^{11}}=$

Step-by-step solution

We are given the expression: $\frac{y^{20}}{y^{11}}$

To solve this, we will use the rule for exponents known as the Power of a Quotient Rule, which states that when you divide two expressions with the same base, you can subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$ .

Applying this rule to our expression:

$\frac{y^{20}}{y^{11}} = y^{20-11}$

After simplifying, we have:

$y^{9}$

The solution to the question is: $y^{9}$

Final Answer

$y^{20-11}$

Key Points to Remember

Essential concepts to master this topic

Quotient Rule: When dividing same bases, subtract the exponents
Technique: $\frac{y^{20}}{y^{11}} = y^{20-11} = y^9$
Check: Multiply back: $y^9 \times y^{11} = y^{20}$ ✓

Common Mistakes

Avoid these frequent errors

Adding exponents instead of subtracting
Don't add the exponents like $y^{20+11} = y^{31}$ ! This gives the multiplication rule result instead of division. Always subtract the bottom exponent from the top exponent when dividing.

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 this way: $\frac{y^{20}}{y^{11}}$ means you have 20 y's multiplied together, then you're dividing by 11 y's. The 11 y's cancel out, leaving you with $20 - 11 = 9$ y's remaining!

What if the bottom exponent is bigger than the top?

You still subtract! For example: $\frac{y^5}{y^8} = y^{5-8} = y^{-3}$ . The negative exponent means one over that positive power: $\frac{1}{y^3}$ .

Does this work with different bases like x and y?

No! The quotient rule only works when the bases are exactly the same. You cannot simplify $\frac{x^5}{y^3}$ using this rule because x and y are different variables.

Can I use this rule with numbers too?

Absolutely! $\frac{3^7}{3^4} = 3^{7-4} = 3^3 = 27$ . The quotient rule works with any base as long as it's the same on top and bottom.

What's the difference between this and multiplying exponents?

When you multiply same bases, you add exponents: $y^5 \times y^3 = y^8$ . When you divide same bases, you subtract exponents: $\frac{y^5}{y^3} = y^2$ .

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