We shall be dealing with the positive and negative integral exponents of a rational numbers.
Let a/b be any rational number and n be a positive integer. Then,
(a/b)ⁿ = a/b × a/b × a/b × ……. n times
= (a × a × a ×…….. n times )/( b × b × b ×……….. n times )
= aⁿ/bⁿ
Thus (a/b)ⁿ = aⁿ/bⁿ for every positive integer n .
For example:
Evaluate:
(i) (3/5)³
= 3³/5³
= 3 × 3 × 3/5 × 5 × 5
= 27/125
(ii) (-3/4)⁴
= (-3)⁴/4⁴
= 34/44
= 3 × 3 × 3 × 3/4 × 4 × 4 × 4
= 81/256
(iii) (-2/3)⁵
= (-2)⁵/3⁵
= (-2)⁵/3⁵
= -2 × -2 × -2 × -2 × -2/3 × 3 × 3 × 3 × 3
= -32/243
Let a/b be any rational number and n be a positive integer.
Then, we define, (a/b)\(^{-n}\) = (b/a)ⁿ
For example:
(i) (3/4)\(^{-5}\)
= (4/3)⁵
(ii) 4\(^{-6}\)
= (4/1)\(^{-6}\)
= (1/4)⁶
Also, we define, (a/b) = 1
Evaluate:
(i) (2/3)\(^{-3}\)
= (3/2)³
= 3³/2³
= 27/8
(ii) 4\(^{-2}\)
= (4/1)\(^{-2}\)
= (1/4)²
= 1²/4²
= 1/16
(iii) (1/6)\(^{-2}\)
= (6/1)²
= 6²
= 36
(iv) (2/3) = 1
The positive and negative integral exponents of a rational numbers are explained here with examples.
● Exponents
Integral Exponents of a Rational Numbers
● Exponents - Worksheets
8th Grade Math Practice
From Integral Exponents of a Rational Numbers 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.
Sep 13, 24 02:48 AM
Sep 13, 24 02:23 AM
Sep 13, 24 01:20 AM
Sep 12, 24 03:07 PM
Sep 12, 24 02:09 AM
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.