7.1/7.2 Nth Roots and Rational Exponents. How do you change a power to rational form and vice versa? How do you evaluate radicals and powers with rational exponents? How do you solve equations involving radicals and powers with rational exponents?. Objectives/Assignment.
How do you change a power to rational form and vice versa?
How do you evaluate radicals and powers with rational exponents?
How do you solve equations involving radicals and powers with rational exponents?
n > 1
The index number becomes the denominator of the exponent.
a > 0 Two real roots
a = 0 One real root
a < 0 No real roots
Change to exponential form.
Change to radical form.
The denominator of the exponent becomes the index number of the radical.
Evaluate without a calculator.
Using radical notation
Using rational exponent notation.
Solve the equation:
Note: index number is even, therefore, two answers.
A. n = 3, a = -125
Solution: Because n = 3 is odd, a = -125 has one real cube root. Because (-5)3 =
-125, you can write:
SOLUTION: First rewrite as . Then enter the following:
To solve simple equations involving xn, isolate the power and then take the nth root of each side.
where m is the mass (in kilograms) of the magnetic sail, f is
the drag force (in newtons) of the spacecraft, and d is the distance (in astronomical units) to the sun. Find the total mass of a spacecraft that can be sent to Mars using m = 5,000 kg, f = 4.52 N, and d = 1.52 AU.
The spacecraft can have a total mass of about 47,500 kilograms. (For comparison, the liftoff weight for a space shuttle is usually about 2,040,000 kilograms.
P = 0.0289s3
A volunteer crew of the Olympias was able to generate a maximum power of about 10.5 kilowatts. What was their greatest speed?
These all work for fraction exponents as well as integer exponents.
= 61/2 + 1/3
= 63/6 + 2/6
b. (271/3 * 61/4)2
= (271/3)2 * (61/4)2
= (3)2 * 62/4
= 9 * 61/2
(43 * 23)-1/3
= (43)-1/3 * (23)-1/3
= 4-1 * 2-1
= ¼ * ½
= 1/8Ex: Simplify. (no decimal answers)
** All of these examples were in rational exponent form to begin with, so the answers should be in the same form!
Two radicals are like radicals, if they have the same index number and radicand
Addition and subtraction is done with like radicals.
Note: same index number and same radicand.
Add the coefficients.
Note: The radicands are not the same. Check to see if we can change one or both to the same radicand.
Note: The radicands are the same. Subtract coefficients.