Unit 3 Review

Square Roots

100

x² = 49

7, -7

200

m² = 400

20, -20

300

t² = 196

14, -14

400

Round to the nearest tenth:

d² = 73

8.5, -8.5

500

Round to the nearest tenth:

y² = 206

14.4, -14.4

Cube Roots

100

y³ = 216

6

200

x³ = -64

-4

300

d³ = 1 / 1331

1 / 11

400

The volume of a cube is 125 in³. How long is each side?

5 in

500

Round to the nearest tenth:

m³ = 225

You may use a calculator to solve.

6.1

Multiplication

100

x² * x⁵

x⁷

200

(2y⁶)⁴

16y²⁴

300

(-7m⁵) * (8m⁹)

-56m¹⁴

400

Are the following equations equivalent to each other for all values of x? Why or why not?

x¹⁸ * x⁵ =

x⁹ * x¹⁴ = 

Yes, as both equations are equal to x²³

500

A company that manufactures faucets uses the formula (2y⁹)³ to calculate the maximum flow rate of water coming out of the faucet. Use the property of exponents to simplify the formula.  

8y²⁷

Division

100

x⁹ / x³

x⁶

200

7m⁹ / 6m⁵

7m⁴ / 6

300

44y³² / 11y¹⁸

4y¹⁴

400

(9x³ / 3x)²

81x⁶ / 9x²  or  9x⁴

500

The amount of bacteria in an infection after taking medication n hours ago is represented by the equation (1 / x³)ⁿ. How much bacteria is in the infection after 6 hours of taking the medication?

1 / x¹⁸

Zero/Negatives

100

y¹⁸ / y¹⁸

1

200

4³ / 4⁵

1 / 4²

300

-4x⁰

-4

400

Is (1 / 4)³ greater than 1, less than 1, or equal to 1?

Less than 1

500

(4d^-4y³)^-2

d⁸ / 16y⁶