explain how rational exponents can be applied to astronomy, homework help

1. Writing in Math Refer to the information on page 435 (attached below) to explain how rational exponents can be applied to astronomy. Explain how to write the formula in radical form and simplify it.

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
r=D where M, is the mass
of the planet, Ms is the mass of the
Sun, and D is the distance between the planet and the Sun.
M
Ms)
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.
(62)2 = b. bż Write the square as multiplication.
=b2+1
Add the exponents.
=bl or b Simplify.
Thus, bż is a number whose square equals b. So bż = Vo.
bin
KEY CONCEPT
Words for any real number b and for any positive integer n, bn = vb,
except when b < 0 and n is even. Example 85 = V8 or 2