EXPRESS THE GIVEN NUMBER IN EXPONENTIAL FORM WORKSHEET

Express the following as the product of prime factors in index form:

Solution

Problem 9 :

Express each of the following products in index form

a) 2 x 2 x 2

b) 4 x 4

c) a x a x a x a

d) k x k x k

e) 10 x 10

f) 2 x 2 x 2 x 2 x 2 x 2

g) b x b x b x b x b

h) y x y x y x y x y x y x y x y

Solution

Problem 10 :

Write the following in expanded form

Solution

Problem 11 :

Evaluate the following

a) 2⁴

c) 3²

b) 5³

d) 1²⁰

Solution

Problem 12 :

Write the prime factors of these numbers in index form

a) 20

c) 36

b) 96

d) 100

Solution

Problem 13 :

Write the following in index form

a) 2 x a x b x a x 2 x a x 2 x b

b) 4d x 2f x 4d x 2f

c) 2cd(2cd)(2cd)(2cd)

d) 3a x 2b x 3a x 2b

e) 5ab(5ab)5b

f) 7ab x 7ab x ab x 7

Solution

Write the prime factorization of the number :

Solution

Problem 11 :

What is the greatest perfect square that is a factor of 1575?

Solution

Problem 12 :

What is the greatest perfect square that is a factor of 396? Explain

Solution

Problem 13 :

Describe and correct the error in writing the prime factorization.

Solution

Problem 14 :

Find the number represented by the prime factorization.

a)  2² ⋅ 3² ⋅ 5

b)  3² ⋅ 5² ⋅ 7

c)  2³ ⋅ 11² ⋅ 13

Solution

Problem 15 :

Find the greatest perfect square that is a factor of the number.

a)  244

b)  650

c)  756

d)  1290

Solution

Problem 15 :

The coach of a baseball team separates the players into groups for drills. Each group has the same number of players. Is the total number of players on the baseball team prime or composite? Explain

Solution

Write each number in index form :

1)  2 × 2 × 3 × 3 x 3

2)  2 × 5 × 5

3)  2 × 3 × 3 × 3 × 5

4)  5 × 5 × 7 × 7

5) 2 × 2 × 5 × 5 × 5 × 7

6)  3 × 3 × 7 × 7 × 11 × 11

7)  2 × 2 × 2 × 3 × 3 × 3 × 3

8)  5 × 5 × 5 × 5 × 5 × 5 × 7 × 7 × 7

Solution

Write the following in exponent form :

1)  25

2) 36

3) 125

4)  343

Solution

Write the following in exponent form with 3 as a base :

1)  3

2)  27

3)  81

4)  729

Solution

Problem 5 :

Evaluate the expression. 

a) 3² + 4²

b) 8² + 15²

c) 13² − 5²

Solution

Problem 6 :

Write each product using exponents.

a) (−7) ⋅ (−7) ⋅ (−7)

b) π ⋅ π ⋅ r ⋅ r ⋅ r

Solution

Problem 7 :

Write the product using exponents.

a)  1/4 ⋅ 1/4 ⋅ 1/4 ⋅ 1/4 ⋅ 1/4

b)  0.3 ⋅ 0.3 ⋅ 0.3 ⋅ 0.3 ⋅ x ⋅ x

Solution

Problem 8 :

Evaluate the expression.

a)  5 + 3 ⋅ 2³

b)  2 + 7 ⋅ (-3)²

c)  (13² - 12²) ÷ 5

d) (1/2) (4³ - 6⋅ 3²)

Solution