Radical Expressions and Rational Exponents
The _______root of a real number a can be written as the ______________________ where n is
the _____________ of the radical and ____ is the _________________.
Numbers & Types of Real Roots
Odd index
_______________
Ex.
Even index
; positive radicand
_______________
Ex.
Even index; negative radicand
_______________
Ex.
Radicand of 0
_______________
Ex.
Ex. 1 Finding real roots
Find all real roots
A.
Fourth roots of 81
B.
Cube roots of -125
C.
Sixth roots of -729
Properties of nth Roots
Product property of roots
The nth root of a ___________ is equal to the product of the _______ roots.
________________ property of roots
The nth root of a ______________ is equal to the quotient of the nth roots.
Ex. 2 Simplifying radical expressions
Simplify each expression. Assume that all variables are positive.
A.
27x6
B.
x3
7
A __________________________ is an exponent that can be expressed as ______, where m and
n are _______________ and ___________. Radical expressions can be written by using rational
____________________.
Ex. 3 Writing expressions in radical form
Write the expression (-125)2/3 in radical form, and simplify.
Ex. 4 Writing expressions by using rational exponents.
A.
B.
Properties of Rational Exponents
Product of powers property
To _____________ powers with the same base, ___________ the exponents.
Quotient of powers property
To _____________ powers with the same base, ______________ the exponents.
Power of a power property
To ___________ one power to another, ______________ the exponents.
Power of a product property
To find the _____________ of a product, __________________ the exponent.
Power of a quotient property
To find the power of a ________________, _______________ the exponent.
Ex. 5 Simplifying expressions with rational exponents
Simplify each expression
A.
B.