Rational Exponents Applications, algebra homework help

1. OPEN ENDED Determine a value of b for which b1/6 is an integer.

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
GET READY for the Lesson
Main Ideas
• Write expressions
with rational
exponents in radical
form and vice versa.
• Simplify expressions
in exponential or
radical form.
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
M,
r =D
M/
M
of the planet, Ms is the mass of the
Sun, and D is the distance between the planet and the Sun.
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.
Write the square as multiplication.
Add the exponents.
= bl or b Simplify.
Thus, bż is a number whose square equals b. So bż = Vo.
bn
KEY CONCEPT
Words for any real number b and for any positive integer n, bi = vb,
except when b < 0 and n is even. Example 85 = V or 2