Chapter 4: Powers and Roots

Powers and exponent's

100

Simplify 

2⁵

2⁵=32

200

Evaluate: (−3)⁴

(−3)⁴ =81

300

Write 8²×8³ as a single power.

8²×8³=8⁵

400

Simplify:5⁶/5²

5⁶/5²=5⁴

500

Evaluate: 3²×3^-1

3²x 3^-1=3¹=3

Roots and Rational Exponents

100

√49

√49=7

200

√144

√144=12

300

Write √16 as a power with an exponent of 1/2.

√16=16 1/2

400

Simplify: 9 1/2

9 1/2=3

500

Write ³√x² using exponents.

³√x²⁼ x 2/3

Laws of Exponent's

100

(2⁴x 2³) / (2⁵)

2⁴x 2³/ 2⁵ = 2^{7 -5}

= 2²

= 4

200

(3x²y)³

(3x²y)³ = 27x⁶y³

300

12x⁵/3x²

12x⁵/3x² = 4x³

400

4m^-2/2m³

4m^-2/2m³ = 2m^-5= 2/m⁵

500

(5a²b^-1)²

(5a²b^-1)² = 25a⁴b^-2= 25a⁴/b²

Word problems

100

A square has an area of 81 cm². What is the length of one side?

Area =81 cm²
Side length =√81= 9 cm

200

A cube has a volume of 125 cm³. What is the length of one edge?

Volume =125 cm³
Edge length =³√125=5 cm

300

The side length of a square is 3x². Write an expression for the area of the square.

(3x²)²= 9x⁴

400

The population of bacteria doubles every hour. If there are initially 200 bacteria, write an expression for the population after 5 hours.

200 x 2⁵

500

A number is multiplied by itself and the result is 196. What is the number?

√196=14