nth Roots and Rational Exponents
Find the indicated real nth root(s) of a.
n=2, a=4
+-2
Simplify using the properties of rational exponents.
5^(1/2)*5^(1/4)
5^(3/4)
Simplify
root(3)(6)*root(3)(36)
6
What do you call this type of function?
f(x)=sqrtx
A square root function
What year was TCHS founded?
1991
Find the indicated real nth root(s) of a.
n=3, a=-64
Simplify using the properties of rational exponents.
10^(5/6)/10^(1/6)
10^(2/3)
root(5)(192)/root(5)(6)
2
What is the domain and range of this function?
f(x)=root(3)x
Domain and range in order:
(-infty,+infty)
(-infty,+infty)
Where did Mr. Alcazar go to college?
UCI and Chapman
(one or the other or both is acceptable)
Find the indicated real nth root(s) of a.
n=4, a=-16
No real nth roots.
Simplify using the properties of rational exponents.
(4^3*5^3)^(-1/3)
1/20
Simplify
1/(6-sqrt2)
(6+sqrt2)/34
Describe the transformations of:
g(x)=2sqrt(x)-5
Vertical stretch (by factor of 2)
Down 5 units
The ages of a father and son add up to 66.
The father's age is the son's age reversed.
How old could they be?
(3 possible solutions).
51 and 15, OR 42 and 24, OR 60 and 06
Solve the equation using nth roots.
5x^3=320
x=4
Simplify using the properties of rational exponents.
(2^(1/4)*3^(1/3))^4
2*3^(4/3)
Simplify.
root(4)(5x^4y^5z^6)
xyzroot(4)(5yz^2)
Describe the transformations.
g(x)=1/4root(3)(-x-4)
Vertical shrink (by factor of 1/4)
Reflection over the y-axis
Right 4 units
What are the two whole, positive numbers that have a one-digit answer when multiplied and two digit answer when added?
1 and 9
Solve the equation using nth roots.
(x+3)^4=24
x~~-0.79 and x~~-5.21
Simplify
(56^(1/4)/8^(1/4))^3
7^(3/4)
Simplify
root(3)(8)/root(3)(x^2)
(2root(3)x)/x
What is the domain and range of:
f(x)=sqrt(x-7)-4
Domain and range in order:
[7,+infty) and [-4,+infty)
Simplify
16root(4)(3p^6)-proot(4)(48p^2)
14proot(4)(3p^2)