Writing in Math Refer to the information on page 415 to explain how rational

Writing in Math Refer to the information on page 415 to explain how rational exponents can be applied to astronomy. Explain how to write the formula r= D in radical form and simplify it.

7-6
Rational Exponents
Main Ideas
Write expressions
with rational
exponents in radical
form and vice versa.
Simplify expressions
in exponential or
radical form.
GET READY for the Lesson
Astronomers refer to the space
around a planet where the planet’s
gravity is stronger than the Sun’s as
the sphere of influence of the planet.
The radius r of the sphere of
influence is given by the formula
Mwhere M, is the mass
M
of the planet, Mş is the mass of the
Sun, and D is the distance between the planet and the Sun.
To
Rational Exponents and Radicals You know that squaring a number
and taking the square root of a number are inverse operations. But how
would you evaluate an expression that contains a fractional exponent
such as the one above? You can investigate such an expression by
assuming that fractional exponents behave as integral exponents.
(1,2)=b2.b write the square as multiplication
=b2+ Add the exponents
= blor b Simplity
Thus, b? is a number whose square equals b. So b = Vb.
KEY CONCEPT
Words for any real number band for any positive integern, bl – Vb.
except when b < and n is even Example 83 - V or 2 EXAMPLE Radical and Exponential Forms a. Write a in radical form. b. Write Vy in exponential form. att Definition of D# V = y^ Definition of bề JISHED Your Progress 14.5 18. Vc Lesson 7-6 Rational Exponents 415