Lesson 59 Using fractional exponents Rational exponents Exponents

Lesson 59 Using fractional exponents

Rational exponents • Exponents of the form m/n, where m and n are integers and n is not 0, are called rational exponents. • Rational exponents can be written as radical expressions.

Rational exponent property • For m and n integers and n is not 0, •

Writing rational exponents as radical expressions

Write as radical expressions

nth roots • • • Radical expressions are called nth roots. n is the index number and a is the radicand If bn = a , then When nth roots have an odd index, there is only one real root. When nth roots have an even index and a positive radicand, there are 2 real roots, one positive and one negative. An nth root with a negative radicand an even index has no real roots.

Properties of nth roots • For a>0, and b>0 • Product property: • Quotient property:

Simplifying radical expressions Factor the radicand into perfect fifths, then apply the product property or quotient property.

Properties of rational exponents • All properties of integer exponents hold true for rational exponents • • Negative exponent rule Zero exponent property Product of powers property Quotient of powers property Power of a power property Power of a product property Power of a quotient property

simplify

Simplifying rational exponents

Simplifying rational exponents

simplify

Solving equations with rational exponents • To cancel out the rational exponent, raise the exponential expression to the reciprocal power.

practice