In rational exponent there are positive rational exponent and negative rational exponent.
We know that 2³ = 8. It can also be expressed as 8\(^{\frac{1}{3}}\) = 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 y\(^{\frac{1}{m}}\) = x but we can write y\(^{\frac{1}{m}}\) = \(\sqrt[m]{y}\) and is called mᵗʰ root of y.
For example, y\(^{\frac{1}{2}}\) = \(\sqrt[2]{y}\), y\(^{\frac{1}{3}}\) = ∛y, y\(^{\frac{1}{4}}\) = ∜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.
x\(^{\frac{p}{q}}\) = \((x^{p})^{\frac{1}{q}}\) = \(\sqrt[q]{x^{p}}\) is read as qᵗʰ root of xᵖ
x\(^{\frac{p}{q}}\) = \((x^{\frac{1}{q}})^{p}\) = \((\sqrt[q]{x})^{p}\) is read as pᵗʰ power of qᵗʰ root of x
For example:
1. Find (125)\(^{\frac{2}{3}}\)
Solution:
(125)\(^{\frac{2}{3}}\)
125 can be expressed as 5 × 5 × 5 = 5³
● 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.
Feb 28, 24 04:07 PM
Feb 28, 24 01:43 PM
Feb 27, 24 02:43 PM
Feb 24, 24 04:11 PM
Feb 24, 24 04:10 PM
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.