APPLYING PROPERTIES OF INTEGER EXPONENTS WORKSHEET

About "Applying properties of integer exponents worksheet"

Applying properties of integer exponents worksheet :

Worksheet on applying properties of integer exponents is much useful to the students who would like to practice problems on simplifying expressions with powers.

We can apply the following properties of integer exponents to simplify expressions with powers. 

Applying properties of integer exponents worksheet - Questions

1.  Simplify the expression given below.

(5-2)⁵ · 3 + (5 + 2)

2.  Simplify the expression given below.

[(3 + 1)²]³ /  (7 - 3)²

3.  Simplify the expression given below.

[(6 - 1)²]² /  (3 + 2)³

4.  Simplify the expression given below.

[(2)²]³ -  (10 - 6)³· 4

Applying properties of integer exponents worksheet - Answers

Question 1 :

Simplify the expression given below.

(5-2)⁵ · 3 + (5 + 2)

Answer : 

Simplify within parentheses.

(5-2)⁵ · 3 + (5 + 2)⁰  =  3⁵ · 3 + 7

Use properties of exponents.

(5-2)⁵ · 3 + (5 + 2)⁰  =  3 + 1

Simplify.

(5-2)⁵ · 3 + (5 + 2)⁰  =  3³ + 1

Apply the rule for negative exponents and add.

(5-2)⁵ · 3 + (5 + 2)⁰  =  1/3³ + 1

(5-2)⁵ · 3 + (5 + 2)⁰  =  1/27 + 1

(5-2)⁵ · 3 + (5 + 2)⁰  =  1 1/27

Question 2 :

Simplify the expression given below.

[(3 + 1)²]³ /  (7 - 3)²

Answer : 

Simplify within parentheses.

[(3 + 1)²]³ /  (7 - 3)²  =  [4²]³ /  4²

Use properties of exponents.

[(3 + 1)²]³ /  (7 - 3)²  =  4 /  4²

Use quotient of powers property.

[(3 + 1)²]³ /  (7 - 3)²  =  4²

Simplify.

[(3 + 1)²]³ /  (7 - 3)²  =  4

[(3 + 1)²]³ /  (7 - 3)²  =  256

Question 3 :

Simplify the expression given below.

[(6 - 1)²]² /  (3 + 2)³

Answer : 

Simplify within parentheses.

[(6 - 1)²]² /  (3 + 2)³  =  [5²]² /  5³

Use properties of exponents.

[(6 - 1)²]² /  (3 + 2)³  =  5 /  5³

Use quotient of powers property.

[(6 - 1)²]² /  (3 + 2)³  =  5³

Simplify.

[(6 - 1)²]² /  (3 + 2)³  =  5¹

[(6 - 1)²]² /  (3 + 2)³  =  5

Question 4 :

Simplify the expression given below.

[(2)²]³ -  (10 - 6)³· 4

Answer : 

Simplify within parentheses.

[(2)²]³ -  (10 - 6)³· 4  =  [4]³ -  4³· 4

Use properties of exponents.

[(2)²]³ -  (10 - 6)³· 4  =  4³ -  4³

Simplify.

[(2)²]³ -  (10 - 6)³· 4  =  4³ -  4²

Apply the rule for negative exponents and simplify.

[(2)²]³ -  (10 - 6)³· 4  =  4³ -  1/4²

[(2)²]³ -  (10 - 6)³· 4  =  64 -  1/16

[(2)²]³ -  (10 - 6)³· 4  =  64/1 - 1/16

[(2)²]³ -  (10 - 6)³· 4  =  (64x16)/(1x16) - 1/16

[(2)²]³ -  (10 - 6)³· 4  =  1024/16 - 1/16

[(2)²]³ -  (10 - 6)³· 4⁻⁵  =  (1024 - 1)/16

[(2)²]³ -  (10 - 6)³· 4⁻⁵  =  1023/16

[(2)²]³ -  (10 - 6)³· 4⁻⁵  =  63 15/16

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