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
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