Properties of Exponents

Product and Quotient of Powers

100

Simplify (2²) (2⁵)

128

200

Simplify (6⁸)/(6⁶)

36

300

Simplify (r³s⁴) (s²t²)

r³s⁶t²

400

Simplify (a⁸)/(a¹⁷)

a^-9 or 1/(a⁹)

500

Simplify (4⁵e⁴f³) (4^-5e^-6f^-1)

(f²)/(e²)

Power of a Power

100

Simplify (4²)²

4⁴ 

^{or 256}

200

Simplify (u¹¹)¹¹

u¹²¹

300

(q¹⁰)⁰

1

400

Simplify (x^-18)³

x^-54 or 1/x⁵⁴

500

Simplify: ((s⁸)⁴))⁵

s¹⁶⁰

Power of a Product and Power of a Quotient

100

Simplify (a³b⁶)⁴

a¹²b²⁴

200

Simplify (3a / 7b)²

(9a²) / (49b²)

300

Simplify (df)² (gh)⁵

d²f²g⁵h⁵

400

Simplify (p⁵/r⁷)⁹

p⁴⁵/r⁶³

500

Simplify (4m⁶n¹⁴)(2m³n⁷)

8m⁹n²¹

Estimating Square Roots

100

 What is the square root of 91?

9.5

200

What is the square root of 7?

2.6

300

What is the square root of 146?

12.1

400

What is the square root of 176?

13.3

500

What is the square root of 84?

9.2

Square root equations

100

x² + 5 = 21

x=4

200

y²+12= 156

y=12

300

3x²-8=19

x=3

400

-2x²+12=-116

x=8

500

5x²=1125

x=15