2.1.2

Rational Exponents

Test yourself

Rational Exponents

Rational exponents are exponents that are fractions, where the numerator is a power and the denominator is a root.

Illustrative background for NotationIllustrative background for Notation ?? "content

Notation

  • There are multiple ways of writing an expression, a variable, or a number with a rational exponent:
    • amn=(a1n)m=(am)1n=amn=(a)ma^{\frac{m}{n}} = (a^{\frac{1}{n}})^{m} = (a^m)^{\frac{1}{n}}=\sqrt[n]{a^m} = (\sqrt{a})^m
Illustrative background for Solving rational exponentsIllustrative background for Solving rational exponents ?? "content

Solving rational exponents

  • To solve rational equations we raise both sides of the equation to the reciprocal of the exponent.
  • This eliminates the exponent on the variable term as any number multiplied by its reciprocal equals 1.
    • This is the same as square rooting both sides of x2=4x^2 = 4 to get x=±2x = \pm 2.
Illustrative background for ExampleIllustrative background for Example ?? "content

Example

  • We want to solve the equation x54=32x^{\frac{5}{4}} = 32.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

Go student ad image

Unlock your full potential with GoStudent tutoring

  • Affordable 1:1 tutoring from the comfort of your home

  • Tutors are matched to your specific learning needs

  • 30+ school subjects covered

Book a free trial lesson