Properties of Exponents (power of power)

4.2 Properties of Exponents (Practice)

Quotient of Powers

Product of Powers

In the previous class, you learned...

Open Ended

Notice and wonder:

1. What do you think $$\left(8^4\right)^3$$ mean?

2. What's the difference between this and $$8^4\cdot8^3$$ ?

3. What's the answer for each of them?

Today, you're going to learn...

As you have looked at the previous slide, in power of power, parentheses are involved. This means that you multiply the exponents. If there are more than one terms inside the parenthesis, you distribute the exponent. (write this down left of the notes)

Power of Power

Multiple Choice

Simplify (x⁵)⁶

• x³⁰

• x¹¹

• x

• 6x¹¹

Math Response

(8⁵)³

Type answer here

Correct Answer: 8^{15}

Deg^°

Rad

Math Response

$$\left(x^{\frac{2}{3}}\right)^4$$

Type answer here

Correct Answer: x^{\frac{8}{3}}

Deg^°

Rad

Multiple Choice

Simplify:
$$(x^{\frac{2}{3}})^{\frac{2}{5}}$$

• x⁴^/¹⁵
• b. x¹⁶^/¹⁵
• c. x⁶
• d. 6x

Multiple Choice

• 4a⁶
• 4a⁵
• -4a⁶
• -4a⁵

Multiple Choice

(2x³y)⁶

• 2x¹⁸y⁶
• 64x¹⁸y⁶
• 64x³y⁶
• 2x³y⁶

Multiple Choice

Simplify (-2m)⁴

• 16m⁴

• -8m⁴

• 16m⁵

• -8m⁵

Multiple Choice

Simplify (-x²y⁴)²

• x⁴y⁸

• -x⁴y⁶

• -2x⁴y⁸

• -2x⁴y⁶

Multiple Choice

Simplify (-2r³p²m)³

• -8r⁹p⁶m³

• -8r⁹p⁶m

• -6r⁶p⁵m⁴

• -6r⁹p⁶m³

Multiple Choice

Simplify (wx⁴z²)⁵

• wx²⁰z¹⁰

• w⁵x²⁰z¹⁰

• w⁶x⁹z⁷

• wx⁹z⁷

Math Response

  Simplify
 (2a²b⁴z)(6a³b²z⁵)

Type answer here

Correct Answer: 12a^5b^6z^6

Deg^°

Rad

Multiple Choice

When you multiply like bases, you ______________the exponents.

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

When you divide like bases, you __________________the exponents.

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

When you raise a power to another power, you ___________________the exponents.

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

Rewrite the radical exponent:

• $$\ ^5\sqrt{x}$$

• $$\ ^1\sqrt{x^5}$$  

• $$\ ^{\ 6}\sqrt{x}$$  

Multiple Choice

Simplify $$\sqrt{50}$$  

• $$5\sqrt{2}$$  

• $$\sqrt{5}$$   

• $$2\sqrt{5}$$  

• $$25\sqrt{2}$$  

Multiple Choice

Simplify $$\sqrt{96}$$

• $$16\sqrt{6}$$  

• $$2\sqrt{6}$$  

• $$4\sqrt{6}$$  

• $$\sqrt{2}$$  

Multiple Choice

Simplify √28m⁴n³

• m²n√7n
• 7m²n√n
• 2m²n√7n
• 7m²n²√n

Hotspot

Click on the part you are confused about.

If you are UNDERSTAND this fully, click on the answer.