Power of a Power

Power of a Power

Quick review on Multiplying Monomials

Multiple Choice

Simplify:

(b⁵)(b⁴)

• $$2b^{54}$$  

• $$b^{20}$$  

• $$b^9$$  

• $$b$$  

• None of these

Multiple Choice

Simplify:

7y⁴  $$\cdot$$ 5y⁸

• $$35y^{32}$$  

• $$35y^{12}$$  

• $$35y^4$$  

• $$35y^2$$  

• None of these

Multiple Choice

Simplify:

(3c²)(10c⁷)

• 13c⁹

• 30c⁵

• 30c⁹

• -30c⁹

Multiple Choice

Simplify:

(6m³n³ )(8m²n³)

• 48m⁵n⁹

• 48m⁶n⁶

• 48m⁵n⁶

• none of the above

New material

How would you solve a problem like this?

​(n²)³

​Think about what this means...

How would you solve this?

Multiple Choice

Simplify:

(r⁴)⁶

• 10r

• r¹⁰

• 24r

• r²⁴

Multiple Choice

Simplify:
(x³)²

• x⁵

• x

• x⁶

• 3x²

Multiple Choice

Simplify:

(5³)⁷

• 5²¹

• 5¹⁰

• 5⁴

• 125²¹

Multiple Choice

Simplify:
(xy²)⁴

• x⁴y²

• x⁴y⁸

• x³y²

• x⁵y⁶

Be careful with these problems!

(xy²)⁴ = (xy²)(xy²)(xy²)(xy²)

= x ⋅ x ⋅ x ⋅ x ⋅ y² ⋅ y² ⋅ y² ⋅ y²

= x⁴ y⁸

​(xy²)⁴ ... what does it mean?

Shortcut for simplifying (xy²)⁴

Multiple Choice

Simplify:
(7y⁴)²

• 7y⁶

• 14y⁸

• 14y⁶

• 49y⁸

Don't forget!

* (7y⁴)² = ​(7¹y⁴)² <-- the "7" has an understood exponent!

= 7²y⁸ <-- re-write 7²

= 49y⁸

Multiple Choice

Simplify: (5ab²)³

• 125a³b⁶

• 15a³b⁶

• 5a³b⁶

• 5ab⁶

Multiple Choice

Simplify (-3x⁴y⁵)²

• 9x⁸y¹⁰

• 6x⁸y¹⁰

• 3x⁸y¹⁰

• -9x⁸y¹⁰