Rational Exponent
In rational exponent there are positive rational exponent and negative rational exponent.
Positive Rational Exponent:
We know that 2³ = 8. It can also be expressed as 813 = 2.
In general if x and yare non-zero rational numbers and m is a positive integer such that xᵐ = y then we can also express it as y1m = x but we can write y1m = m√y and is called mᵗʰ root of y.
For example, y12 = 2√y, y13 = ∛y, y14 = ∜y, etc. If x is a positive rational number then for a positive ration exponent p/q we have x₀can be defined in two equivalent form.
xpq = (xp)1q = q√xp is read as qᵗʰ root of xᵖ
xpq = (x1q)p = (q√x)p is read as pᵗʰ power of qᵗʰ root of x
For example:
1. Find (125)23
Solution:
(125)23
125 can be expressed as 5 × 5 × 5 = 5³
2. Find (8/27)4/3
Solution:
(8/27)4/3
8 = 23 and 27 = 33
So, we have (8/27)4/3 = (23/33)4/3
= [(2/3) 3]4/3
= (2/3)
= (2/3) 4
= 2/3 × 2/3 × 2/3 × 2/3
= 16/81
3. Find 91/2
Solution:
91/2
= √(2&9)
= [(3)2]1/2
= (3)
= 3
4. Find 1251/3
Solution:
1251/3
= ∛125
= [(5) 3]1/3
= (5)
= 5
Negative Rational Exponent:
We already learnt that if x is a non-zero rational number and m is any positive integer then x-m = 1/xm = (1/x)m, i.e., x-m is the reciprocal of xm.Same rule exists of rational exponents.
If p/q is a positive rational number and x > 0 is a rational number
Then x-p/q = 1/xp/q = (1/x) p/q, i.e., x-p/q is the reciprocal of xp/q
If x = a/b, then (a/b)-p/q = (b/a)p/q
For example:
1. Find 9-1/2
Solution:
9-1/2
= 1/91/2
= (1/9)1/2
= [(1/3)2]1/2
= (1/3)
= 1/3
2. Find (27/125)-4/3
Solution:
(27/125)-4/3
= (125/27)4/3
= (53/33)4/3
= [(5/3) 3]4/3
= (5/3)
= (5/3)4
= (5 × 5 × 5 × 5)/(3 × 3 × 3 × 3)
= 625/81
● Exponents
Integral Exponents of a Rational Numbers
● Exponents - Worksheets
8th Grade Math Practice
From Rational Exponent to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Counting Numbers from 1 to 50 | Match the Number | Missing Numbers
Apr 04, 25 03:46 PM
In counting numbers from 1 to 50, recognize the numbers, count and then join the numbers in the correct number order. Here we mainly need eye-hand coordination to draw the picture and maintain the num -
Counting Eleven to Twenty with Numbers and Words |Numbers from 11 - 20
Apr 04, 25 03:21 PM
Counting eleven to twenty with numbers and words are explained below. One ten and one more is eleven. Eleven comes after ten. One ten and two more is twelve. Twelve comes after eleven. -
5th Grade BODMAS Rule Worksheet | PEMDAS | Order of operations|Answers
Apr 03, 25 03:11 PM
In 5th Grade BODMAS Rule Worksheet you will get different types of problems on mathematical expressions involving different operations, mathematical expression with 'brackets' and 'of' and simplifying… -
Worksheet on Simplification | Simplify Expressions | BODMAS Questions
Apr 03, 25 02:58 PM
In worksheet on simplification, the questions are based in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. This exercise sheet -
Divisible by 2 Video |Test of Divisibility by 2 Trick| Rules| Examples
Apr 03, 25 10:25 AM
A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.