# APPLYING PROPERTIES OF INTEGER EXPONENTS

## About "Applying properties of integer exponents"

Applying properties of integer exponents :

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

## Applying properties of integer exponents - Examples

Example 1 :

Simplify the expression given below.

(5-2)⁵ · 3 + (5 + 2)

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

Example 2 :

Simplify the expression given below.

[(3 + 1)²]³ /  (7 - 3)²

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

Example 3 :

Simplify the expression given below.

[(6 - 1)²]² /  (3 + 2)³

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

Example 4 :

Simplify the expression given below.

[(2)²]³ -  (10 - 6)³· 4

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

After having gone through the stuff given above, we hope that the students would have understood how to apply properties of integer exponents

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