Evaluating roots

 $Which\ \exp ression\ is\ equivalent\ to\ 2\left(5\right)^4$ ? 

• 2 x 5 x 4

• 2 x 5 x 5 x 5 x 5

• 2 x 4 x 4 x 4 x 4 x 4

• 10 x 10 x 10 x 10

Answer explanation

Power of a Power, means multiply the exponents

 $3^5$  

Check all correct answers.

• five cubed

• three raised to the fifth power

•  $3\times3\times3\times3\times3$  

• 81

Simplify the following radical: √32

• 3√2
• 4√8
• 16√2
• 4√2

Write in exponential form.

8x8x8

• 64

• 512

What is the value of (-1)⁶?

• -1  

• 6

• -6

• 1 

Answer explanation

Since the exponent is an even number, raising -1 to the power of 6 will result in a positive number. In this case, (-1)⁶ means multiplying -1 by itself six times: (-1) × (-1) × (-1) × (-1) × (-1) × (-1) = 1.

Simplify.

Multiply and remove all perfect squares from inside the square roots.  Assume b is positive.
 $\sqrt{24b^3}\cdot\sqrt{40b^2}\cdot\sqrt{b^2}$  

•  $34b^2$  

•  $8b^2\sqrt{15b}$  

•  $\sqrt{64b^7}$  

•  $8b^3\sqrt{15b}$  

Express the answer in simplest radical form.

• $8x^3y^3\ \ \ \ ^3\sqrt{2x^2y}$

• $2x^3y^5\ \ \ \ ^3\sqrt{2x^2y}$

• $4x^3y^5\ \ \ \ ^3\sqrt{x^2y}$

• $2x^3y^3\ \ \ \ ^3\sqrt{2x^2y^2}$