Radical Expressions and Rational Exponents Flashcards
What does the exponent 1/n indicate?
This exponent indicates the nth root.
What is a Rational Exponent?
A rational exponent that can be expressed as m/n, where m and n are integers, and n cannot equal 0. The exponent m/nindicates the nth root raised to the mth power.
How do you simplify Rational Exponents?
You convert them to radical form and then simplify or solve.
How do you convert Radicals to Rational Form?
You write the radicand with a rational exponent with the numerator as the power of the radicand. The denominator is the index of the radical.
How does the nth root work?
The nth root of a real number a can be written as the radical expression ^n(sqrt a), where n is the index of the radical and a is the radicand.
How do you solve nth root problems?
You change “nth root of y” to “x^nth=y.”
How do you Rationalize the Denominator?
You rewrite the expression so that the denominator contains no radicals.
What is the formula for Product of Powers?
a^m*a^n=a^m+n.
What is the formula for Quotient of Powers?
a^m/a^n=a^m-n.
What is the formula for Power of a Power?
(a^m)^n=a^mn.
What is the formula for Power of a Product?
(ab)^m=(a^m)(b^m).
What is the formula for Power of a Quotient?
(a/b)^m=(a^m)/(b^m).
