8.2 Lesson on Power of a Quotient Rule

Power of a Quotient Property

By Blake Jensen

Multiple Choice

What does quotient mean?

• Multiply

• Divide

• Add

• Subtract

Hotspot

Click on the Powers!
(Even the hidden ones)

Math Response

Simplify the following!

(3x²y³z)⁴

Type answer here

Correct Answer: 81x^8y^{12}z^4

Deg^°

Rad

Everything has its own exponent

Distribute to all exponents inside!

The power to a power rule means you must multiply all powers inside by what is outside. This only works for a single term! Try the following


(4x²y⁴z³)³

Open Ended

Talk with your neighbors! How would you solve the following?

$$\left(\frac{2x^6y^3z}{4x^5y^5z^3}\right)^5$$

Power of a Quotient

Reduce, then multiply to top and bottom exponents

Careful!

Here we distribute first because of grouping.
Then reduce if possible.