Properties of Exponents
Simplify the expression:
8^5 * 8^8
8^13
6c^4 * 8c^3
48c^7
What two integers is sqrt(15) between?
It is between 3 and 4.
(Explanation: 3^2 = 9 , which is less than 15, and 4^2 = 16 , which is greater than 15.)
Put these numbers in order from least to greatest.
sqrt(2), 5, sqrt(18), root(3)27, sqrt(81)
sqrt(2), root(3)27, sqrt(18), 5, sqrt(81)
Is this number rational or irrational?
37 / 50
Rational
(Because it is a fraction.)
Simplify the expression:
(47^22)/(47^16)
47^6
"Solve for y."
(27m^y)/(9m^2) = 3m^3
y = 5
What two integers is sqrt(150) between?
It is between 12 and 13.
(Explanation: 12^2 = 144 , which is less than 180, and 13^2 = 169 , which is greater than 180.)
Put these numbers in order from least to greatest.
root(3)(125), 4, pi, 2^3, sqrt(20)
pi, 4, sqrt(20), root(3)(125), 2^3
Is this number rational or irrational?
17.3892
Rational
17.3892 = 17 3892 / 10000
Simplify the expression:
x^-81
1/x^81
(65z^2) / (26z^6)
(5) / (2z^4)
What two integers is root(3)(40) between?
It is between 3 and 4.
(Explanation: 3^3 = 27 , which is less than 40, and 4^3 = 64 , which is greater than 40.)
Put these numbers in order from least to greatest.
sqrt(121), root(3)(64), sqrt(80), 7, root(3)100
root(3)(64), root(3)(100), 7, sqrt(80), sqrt(121)
Is this number rational or irrational?
sqrt(2)
Irrational.
sqrt(2) = 1.414213...
Simplify the expression:
729^3 / 729^8
1 / 729^5
Solve for x.
(27b^6) / (sqrt(81b^x)) = 3 / b^2
x = 16
What two integers is root(3)(250) between?
It is between 6 and 7.
(Explanation: 6^3 = 216 , which is less than 250, and 7^3 = 343 , which is greater than 250.)
Put these numbers in order from least to greatest.
sqrt(7), root(3)(8), 9, sqrt(20), root(3)(30)
root(3)(8), sqrt(7), root(3)(30), sqrt(20), 9
Is this number rational or irrational?
sqrt(1/4)
Rational.
sqrt(1/4) = 1/2
Solve for y.
x^18 div x ^y = x^23
y = -5
root(3)(54r^11 *4r^4s^3)
6r^5s
What two integers is root(4)(10) between?
It is between 1 and 2.
(Explanation: 1^4 = 1 , which is less than 10, and 2^4 = 16 , which is greater than 10.)
Put these numbers in order from least to greatest.
sqrt(2), root(3)(8), sqrt(9), sqrt(15), root(3)(25)
sqrt(2), root(3)(8), root(3)(25), sqrt(9), sqrt(15)
Is this number rational or irrational?
sqrt(50)
Irrational.
sqrt(50) = 5(sqrt2) = 7.071067...