7­4 Rational Exponents 2011
March 31, 2011
Use a calculator to find each value. Look for a patte
1
2
1. 25 =
1
2
2. 100 =
0.5
3. 81 =
1
2
4. 49 =
5
2
5. 4 =
1
3
6. 27 =
1
3
7. 64 =
1
3
8. 8 =
2
3
9. 27 =
2
3
10. 8 =
1
7­4 Rational Exponents 2011
March 31, 2011
7­4 Rational Exponents
Objectives:
Convert between rational exponents and radical form.
Use rational exponents to solve real world situations.
Simplify expressions with rational exponents.
2
7­4 Rational Exponents 2011
March 31, 2011
x
m
n
x
m
n
power
root
base
=
25
3
4
27
16
n
= 25
= 27
= 16
x
m
1
2
1
3
1
4
3
7­4 Rational Exponents 2011
March 31, 2011
3
4
x = ∜x 3
4
7­4 Rational Exponents 2011
March 31, 2011
Write the exponential expressions in radical form.
x
5
3
y
0.4
z
­ 14
5
7­4 Rational Exponents 2011
March 31, 2011
Write the radical expressions in exponential form.
√a3
5
2
(√ b)
(√y)3
6
7­4 Rational Exponents 2011
March 31, 2011
Space Travel
Bone loss for astronauts on lengthy space voyages may be prevented with a bedlike apparatus that rotates to simulate the effect of gravity. In the formula
N = a0.5
2πr0.5
N is the rate of rotation in revolutions per second, a is the simulated acceleration in m/s2 , and r is the radius of the apparatus in meters. How fast would an apparatus with a radius of 1.7 m have to rotate in simulate the acceleration of 9.8 m/s2 that is due to Earth's gravity?
7
7­4 Rational Exponents 2011
March 31, 2011
Homework:
page 388
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