Algebra Rational Exponents

Algebra is one of the most basic element of mathematics in which, we switch from basic arithmetic to variables.  Algebra covers a large number of subdivisions like polynomials, rational, exponents, logarithms, expressions etc under it. Exponents are in the form of 'ab ' where a is the base and b is the power (exponent). Exponents in rational form are called as rational exponents. For example: a 1/2 , 'a' has a rational exponent of 1/2. The rules , representation and examples on algebra ational exponents is given in the following sections.

Rational Exponents:

As said earlier rational exponents are in the form  ab/c, where b/c is the rational exponent. Algebra rational exponents can be represented in the following ways.

root(n)(x)  = x^(1/n)

root(3)(x)  = x^(1/3)

root(3)(x^2)  = x^(2/3)

an = b  ===>  a = b^(1/n)

Examples on Rational exponents:

ALgebra Example 1:

Simplify the expression(root(3)(2^3))^4

Solution:

The given expression is (root(3)(2^3))^4

It can be represented as  ((2^3)^(1/3) )4

Therefore, (2^(3/3) )4

= 24

= 2*2*2*2 = 16

Therefore, The simplified answer for the expression is 16.

Algebra Example 2:

Simplify the expression(root(2)(2^3))^4

Solution:

The given expression is (root(2)(2^3))^4

It can be represented as  ((2^3)^(1/2) )4

Therefore, (2^(3/2) )4

= 2^(12/2)

= 26 = 2*2*2*2*2*2 = 64

Therefore, The simplified answer for the expression is 64.

Algebra Example 3:

Simplify the expression(root(2)(2^3))^2

Solution:

The given expression is (root(2)(2^3))^2

It can be represented as  ((2^3)^(1/2) )2

Therefore, (2^(3/2) )2

= 2^(6/2)

= 23 = 2*2*2 = 8

Therefore, The simplified answer for the expression is 8.

Practice problems on rational exponents:

Here are few practice problems given to make sure that the students have learned  the  above mentioned rational exponents concept,

1. Simplify the expression root(5)(x) = 2 , and find the value of 'x'

2. SImplify the expression root(3)(27)

Solution:

1. x =32

2. 3