USING DISTRIBUTIVE PROPERTY WITH RATIONAL EXPONENTS

Subscribe to our 鈻讹笍 YouTube channel 馃敶 for the latest videos, updates, and tips.

For example, 

a(b + c) = ab + ac

When it involves rational exponents, we have to know about rules in exponents.

productruleofexponents

Expand and simplify :

Problem 1 :

2x123x32 - 4x-12

Solution :

2x123x32 - 4x-12

Use the distributive property.

=2x123x32 - 2x124x-12

Using properties of exponents, we get

= 6x12 + 32 - 8x12 + -12= 6x42 - 8x12 - 12= 6x2 - 8x0= 6x2 - 8

Problem 2 :

x12x12 - x-12

Solution :

x12x12 - x-12

Use the distributive property.

=x12x12 - x12x-12

Using properties of exponents, we get

= x12 + 12 - x12 + -12= x22 - x12 - 12= x1 - x0= x - 1

Problem 3 :

x-12x12 - 2x-12

Solution :

x-12x12 - 2x-12

Use the distributive property.

=x-12x12 - x-122x-12

Using properties of exponents, we get

= x-12 + 12 - 2x-12 + -12= x0 - 2x-12 - 12= 1 - 2x-22= 1 - 2x-1= 1 - 2 1x= 1 - 2x= x - 2x

Problem 4 :

x322x12 - x-12

Solution :

x322x12 - x-12

Use the distributive property.

=x322x12 - x32x-12

Using properties of exponents, we get

= 2x32 + 12 - x32 + -12= 2x42 - x32 - 12= 2x2 - x22= 2x2 - x1= 2x2 - x= x(2x - 1)

Problem 5 :

x12 + 3 x12 - 3

Solution :

x12 + 3 x12 - 3

Use the distributive property.

= x12 x12 - 3 x12 + 3 x12 - 3 3

Using properties of exponents, we get

= x12 + 12 - 9= x22 - 9= x - 9

Problem 6 :

x12 + x-12 x12 - x-12

Solution :

x12 + x-12 x12 - x-12

Use the distributive property.

= x12 x12 - x12 x-12 + x-12 x12 - x-12 x-12

Using properties of exponents, we get

= x12 x12 - x-12 x-12= x12 + 12 - x-12 - 12= x22 - x-22= x1 - x-1= x - 1x= x2 - 1x

Problem 7 :

x + 3x2

Solution :

x + 3x2

Use the distributive property.

= x + 3xx + 3x

Using properties of exponents, we get

= x2 + x 3x + x 3x + 3x 3x= x2 + 3 + 3 + 9x2= x2 + 9x2 + 6

Subscribe to our 鈻讹笍 YouTube channel 馃敶 for the latest videos, updates, and tips.

Recent Articles

  1. Finding Range of Values Inequality Problems

    May 21, 24 08:51 PM

    Finding Range of Values Inequality Problems

    Read More

  2. Solving Two Step Inequality Word Problems

    May 21, 24 08:51 AM

    Solving Two Step Inequality Word Problems

    Read More

  3. Exponential Function Context and Data Modeling

    May 20, 24 10:45 PM

    Exponential Function Context and Data Modeling

    Read More