Chapter 4:Exponents and Radicals

Prime factorization

100

What is the prime factorization of 729?

Answer: 9

200

Can 196 be broken down into a square root or a cube root? If so, what are the answers?

Square root: 14

300

What is the largest prime factor for 462

Answer: 11

400

Can 4096 be broken down into a square root or a cube root? If so, what are the answers?

Cube root: 16
Square root: 64

500

The cube root of 4,913

Cube root: 17

Exponent Laws

100

Using exponent laws, simplify this expression (3²)³

Answer: 729 or 3⁶

200

Using exponent laws, simplify this expression 3² x 3⁶

Answer: 6561 or 3⁸

300

Using exponent laws, simplify this expression (4^-1)^-3

Answer: 64 or 4³

400

Using exponent laws, simplify this expression (4/16)³

Answer: 1/4

500

Using exponent laws, simplify this expression [4x^-2/9y^-4]^-5/2

Answer: [3x/2y²]⁵

Radicals

100

Convert this mixed radical as an entire radical 3√2

= √18

200

Write this power in radical form 8 5/3.

Radical form: ³√ 8⁵

300

Write this entire radical in simplest form ⁴√625

Answer: 5

400

Write this power in radical form (1/4)^3/2

Radical form: 1/√64

500

Use exponent laws to simplify [x^-2/(xy)⁴]^1.5

Answer: 1/x⁹y⁶

BONUS!!

100

What is the square root of 2401?

Answer: 49

200

what is the sum of 2³x√(16) 

32

300

Can 16,384 be broken down into a square root or a cube root? If so, what are the answers?

Answer: 128

400

Simplify this expression √126

Answer: 3√14

500

Simplify this expression 5⁴√3

Answer: 1875